|Precursor||lateral plate mesoderm|
The limb bud is a structure formed early in vertebrate limb development. As a result of interactions between the ectoderm and underlying mesoderm, formation occurs roughly around the fourth week of development.  In the development of the human embryo the upper limb bud appears in the third week and the lower limb bud appears four days later. 
The limb bud consists of undifferentiated mesoderm cells that are sheathed in ectoderm.  As a result of cell signaling interactions between the ectoderm and underlying mesoderm cells, formation of the developing limb bud occurs as mesenchymal cells from the lateral plate mesoderm and somites begin to proliferate to the point where they create a bulge under the ectodermal cells above.  The mesoderm cells in the limb bud that come from the lateral plate mesoderm will eventually differentiate into the developing limb’s connective tissues, such as cartilage, bone, and tendon.  Moreover, the mesoderm cells that come from the somites will eventually differentiate into the myogenic cells of the limb muscles. 
The limb bud remains active throughout much of limb development as it stimulates the creation and positive feedback retention of two signaling regions: the apical ectodermal ridge (AER) and the zone of polarizing activity (ZPA) with the mesenchymal cells.  These signaling centers are crucial to the proper formation of a limb that is correctly oriented with its corresponding axial polarity in the developing organism. Research has determined that the AER signaling region within the limb bud determines the proximal-distal axis formation of the limb using FGF signals.  ZPA signaling establishes the anterior-posterior axis formation of the limb using Shh signals.  Additionally, though not known as a specific signaling region like AER and ZPA, the dorsal-ventral axis is established in the limb bud by the competitive Wnt7a and BMP signals that the dorsal ectoderm and ventral ectoderm use respectively.   Because all of these signaling systems reciprocally sustain each other’s activity, limb development is essentially autonomous after these signaling regions have been established. 
The Hox genes, which define features along the anterior-posterior axis of a developing organism, determine at which points along the axis that limb buds will form.  Though limbs emerge at different locations in different species, their positions always correlate with the level of Hox gene expression along the anterior-posterior axis.  All limb buds must also rely on other signaling factors to obtain their forelimb or hindlimb identity; Hox gene expression influences expression of T-box proteins that, in turn, determine limb identity for certain organisms. 
In turn, the activation of T-box protein activates signaling cascades that involve the Wnt signaling pathway and FGF signals.  Before limb development begins, T-box proteins initiate FGF10 expression in the proliferating mesenchymal cells of the lateral plate mesoderm, which form the limb bud mesoderm.  WNT2B and WNT8C stabilize this FGF10 expression in the forelimb and hindlimb, respectively.   This FGF10 expression stimulates WNT3 expression in the above ectodermal cells – resulting in formation of the apical ectodermal ridge as well as inducing FGF8 expression.  The FGF8 secreted by the AER acts to keep the cells of the limb mesenchyme in a mitotically active state and sustains their production of FGF10.  positive feedback loop between the limb mesenchymal cells and the AER maintains the continued growth and development of the entire limb. 
In addition to limb outgrowth, the formation of a crucial signaling center, the zone of polarizing activity (ZPA), in a small posterior portion of the limb bud helps to establish anterior-posterior polarity in the limb through secretion of the protein Sonic hedgehog (Shh).  The ZPA also plays an important role in initially specifying digit identity, while later maintaining proper AER morphology and continued FGF8 secretion – to ensure proper mitotic activity of the limb bud mesenchyme beneath. 
In chickens, Tbx4 specifies hindlimb status, while Tbx5 specifies forelimb status.  In mice, however, both hindlimbs and forelimbs can develop in the presence of either Tbx4 or Tbx5.  In fact, it is the Pitx1 and Pitx2 genes that appears to be necessary for specification of the developing hindlimb, whereas their absence results in forelimb development.  Tbx4 and Tbx5 appear to be important specifically for limb outgrowth in mice. 
Within the limb bud, expression of specific Hox genes varies as a function of the position along the anterior-posterior axis. The Hox genes are linked in four chromosomal clusters: Hoxa, Hoxb, Hoxc, and Hoxd.  Their physical position on the chromosome correlates with the time and place of expression. This statement is supported by the knowledge that Hox gene expression is initiated during gastrulation in primitive somitic mesoderm by FGF signaling which effects the primitive somitic mesoderm cells at different times depending on their axial location during organism development—and is even further specified with other anterior-posterior axis signals (such as retinoic acid).  Additional evidence for the role that Hox genes play in limb development was found when researchers effected Hox gene expressions in zebrafish by adding retinoic acid during gastrulation; This experiment resulted in a duplication of limbs.  Although excess retinoic acid can alter limb patterning by ectopically activating Shh expression, genetic studies in mouse that eliminate retinoic acid synthesis have shown that RA is not required for limb patterning. 
Chicken development is a wonderful example of this specificity of Hox gene expression in regard to limb development. The most 3’ Hoxc genes (HOXC4, HOXC5) are expressed only in the anterior limbs in chickens, while the more 5’ genes (HOXC9, HOXC10, HOXC11) are expressed only in the posterior limbs.  The intermediate genes (HOXC6, HOXC8) are expressed in both the upper and lower limbs in chickens. 
As previously stated, limb development is essentially autonomous after the signaling centers (AER) and ZPA) have been established. However, it is important to know that Hox genes continue to participate in the dynamic regulation of limb development even after the AER and ZPA have been established in the limb bud. Complex communication ensues as AER-secreted FGF signals and ZPA-secreted Shh signals initiate and regulate Hox gene expression in the developing limb bud.  Though many of the finer details remain to be resolved, a number of significant connections between Hox gene expression and the impact on limb development have been discovered.
The pattern of Hox gene expression can be divided up into three phases throughout limb bud development, which corresponds to three key boundaries in proximal-distal limb development. The transition from the first phase to the second phase is marked by the introduction of Shh signals from the ZPA.  The transition into the third phase is then marked by changes in how the limb bud mesenchymal cells responds to Shh signals.  This means that although Shh signaling is required, its effects change over time as the mesoderm is primed to respond to it differently.  These three phases of regulation reveal a mechanism by which natural selection can independently modify each of the three limb segments – the stylopod, the zeugopod, and the autopod. 
By mimicking the initial FGF10 secretions of the lateral plate mesoderm cells, limb development can be initiated. Other signaling molecules are implicated in determining the limb's identity.
HOXD11 is expressed posteriorly, near the ZPA, where the highest levels of Shh signal expression occur.
These experiments reveal that the limb mesenchyme contains the necessary information concerning limb identity, but the AER is needed to stimulate the mesenchyme to live up to its destiny (of becoming an arm, leg, etc.)
The ZPA first specifies anterior-posterior polarity (and dictates digit identity), and then, by sustaining AER activity, it ensures that the necessary cell proliferation occurs for normal formation of a five-digit limb.
Associated molecules include: 
Somitogenesis is the process by which somites form. Somites are bilaterally paired blocks of paraxial mesoderm that form along the anterior-posterior axis of the developing embryo in segmented animals. In vertebrates, somites give rise to skeletal muscle, cartilage, tendons, endothelium, and dermis.
Intermediate mesoderm or intermediate mesenchyme is a narrow section of the mesoderm located between the paraxial mesoderm and the lateral plate of the developing embryo. The intermediate mesoderm develops into vital parts of the urogenital system, as well as the reproductive system.
Lateral plate mesoderm is a type of mesoderm that is found at the periphery of the embryo.
The apical ectodermal ridge (AER) is a structure that forms from the ectodermal cells at the distal end of each limb bud and acts as a major signaling center to ensure proper development of a limb. After the limb bud induces AER formation, the AER and limb mesenchyme—including the zone of polarizing activity (ZPA)—continue to communicate with each other to direct further limb development.
Limb development in vertebrates is an area of active research in both developmental and evolutionary biology, with much of the latter work focused on the transition from fin to limb.
Gremlin is an inhibitor in the TGF beta signaling pathway. It primarily inhibits bone morphogenesis and is implicated in disorders of increased bone formation and several cancers.
T-box refers to a group of transcription factors involved in embryonic limb and heart development. Every T-box protein has a relatively large DNA-binding domain, generally comprising about a third of the entire protein that is both necessary and sufficient for sequence-specific DNA binding. All members of the T-box gene family bind to the "T-box", a DNA consensus sequence of TCACACCT.
T-box transcription factor TBX5 is a protein that in humans is encoded by the TBX5 gene.
Fibroblast growth factor 8 is a protein that in humans is encoded by the FGF8 gene.
T-box transcription factor 2 Tbx2 is a transcription factor that is encoded by the Tbx2 gene on chromosome 17q21-22 in humans. This gene is a member of a phylogenetically conserved family of genes that share a common DNA-binding domain, the T-box. Tbx2 and Tbx3 are the only T-box transcription factors that act as transcriptional repressors rather than transcriptional activators, and are closely related in terms of development and tumorigenesis. This gene plays a significant role in embryonic and fetal development through control of gene expression, and also has implications in various cancers. Tbx2 is associated with numerous signaling pathways, BMP, TGFβ, Wnt, and FGF, which allow for patterning and proliferation during organogenesis in fetal development.
Protein odd-skipped-related 1 is a transcription factor that in humans is encoded by the OSR1 gene. The OSR1 and OSR2 transcription factors participate in the normal development of body parts such as the kidney.
The zone of polarizing activity (ZPA) is an area of mesenchyme that contains signals which instruct the developing limb bud to form along the anterior/posterior axis. Limb bud is undifferentiated mesenchyme enclosed by an ectoderm covering. Eventually, the limb bud develops into bones, tendons, muscles and joints. Limb bud development relies not only on the ZPA, but also many different genes, signals, and a unique region of ectoderm called the apical ectodermal ridge (AER). Research by Saunders and Gasseling in 1948 identified the AER and its subsequent involvement in proximal distal outgrowth. Twenty years later, the same group did transplantation studies in chick limb bud and identified the ZPA. It wasn't until 1993 that Todt and Fallon showed that the AER and ZPA are dependent on each other.
Diplopodia is a congenital anomaly in tetrapods that involves duplication of elements of the foot on the hind limb. It comes from the Greek roots diplo = "double" and pod = "foot". Diplopodia is often found in conjunction with other structural abnormalities and can be lethal. It is more extreme than polydactyly, the presence of extra digits.
The order Chiroptera, comprising all bats, has evolved the unique mammalian adaptation of flight. Bat wings are modified tetrapod forelimbs. Because bats are mammals, the skeletal structures in their wings are morphologically homologous to the skeletal components found in other tetrapod forelimbs. Through adaptive evolution these structures in bats have undergone many morphological changes, such as webbed digits, elongation of the forelimb, and reduction in bone thickness. Recently, there have been comparative studies of mouse and bat forelimb development to understand the genetic basis of morphological evolution. Consequently, the bat wing is a valuable evo-devo model for studying the evolution of vertebrate limb diversity.
The Cdx gene family, also called caudal genes, are a group of genes found in many animal genomes. Cdx genes contain a homeobox DNA sequence and code for proteins that act as transcription factors. The gene after which the gene family is named is the caudal or cad gene of the fruitfly Drosophila melanogaster. The human genome has three Cdx genes, called CDX1, CDX2 and CDX4. The zebrafish has no cdx2 gene, but two copies of cdx1 and one copy of cdx4. The Cdx gene in the nematode Caenorhabditis elegans is called pal-1.
The clock and wavefront model is a model used to describe the process of somitogenesis in vertebrates. Somitogenesis is the process by which somites, blocks of mesoderm that give rise to a variety of connective tissues, are formed.
Hox genes play a massive role in some amphibians and reptiles in their ability to regenerate lost limbs, especially HoxA and HoxD genes.
T-box transcription factor Tbx4 is a transcription factor that belongs to T-box gene family that is involved in the regulation of embryonic developmental processes. The transcription factor is encoded by the TBX4 gene located on human chromosome 17. Tbx4 is known mostly for its role in the development of the hindlimb, but it also plays a critical role in the formation of the umbilicus. Tbx4 has been shown to be expressed in the allantois, hindlimb, lung and proctodeum.
Homeobox protein CDX-4 is a protein that in humans is encoded by the CDX4 gene. This gene is a member of the caudal-related homeobox transcription factor family that also includes CDX1 and CDX2.