A valvetrain or valve train is a mechanical system that controls the operation of the intake and exhaust valves in an internal combustion engine.  The intake valves control the flow of air/fuel mixture (or air alone for direct-injected engines) into the combustion chamber, while the exhaust valves control the flow of spent exhaust gasses out of the combustion chamber once combustion is completed. 
The valvetrain layout is largely dependent on the location of the camshaft(s). The common valvetrain configurations for piston engines - in order from oldest to newest - are:
The valvetrain consists of all the components responsible for transferring the rotational movement of the camshaft into the opening and closing of the intake and exhaust valves. Typical components are listed below in order from the crankshaft to the valves.
The timing and lift profile of the valve opening events are controlled by the camshaft, through use of a carefully shaped lobe on a rotating shaft. The camshaft is driven by the crankshaft and— in the case of a four-stroke engine— rotates at half the speed of the crankshaft.
Motion is transferred from the crankshaft to the camshaft most commonly by a rubber timing belt, a metallic timing chain or a set of gears.
Pushrods are long, slender metal rods that are used in overhead valve engines to transfer motion from the camshaft (located in the engine block) to the valves (located in the cylinder head). The bottom end of a pushrod is fitted with a lifter, upon which the camshaft makes contact. The camshaft lobe moves the lifter upwards, which moves the pushrod. The top end of the pushrod pushes on the rocker arm, which opens the valve.
Depending on the design used, the valves are actuated by a rocker arm, finger or bucket tappet. Overhead valve engines use rocker arms, which are actuated from below indirectly (through the pushrods) by the cam lobes. Overhead camshaft engines use fingers or bucket tappets, which are actuated from above directly by the cam lobes. 
Most modern engines use poppet valves, although sleeve valves, slide valves and rotary valves have also been used at times. Poppet valves are typically opened by the camshaft lobe or rocker arm, and closed by a coiled spring called a valve spring.
Valve float occurs when the valve spring is unable to control the inertia of the valvetrain at high engine speeds (RPM).  
A poppet valve is a valve typically used to control the timing and quantity of gas or vapor flow into an engine.
The camshaft is a rotating object— usually made of metal— that contains pointed cams, which converts rotational motion to reciprocal motion. Camshafts are used in internal combustion engines, mechanically controlled ignition systems and early electric motor speed controllers. Camshafts in automobiles are made from steel or cast iron, and are a key factor in determining the RPM range of an engine's power band.
The engine configuration describes the fundamental operating principles by which internal combustion engines are categorized.
In an internal combustion engine, the cylinder head sits above the cylinders and forms the roof of the combustion chamber.
A desmodromic valve is a reciprocating engine poppet valve that is positively closed by a cam and leverage system, rather than by a more conventional spring.
VTEC is a system developed by Honda to improve the volumetric efficiency of a four-stroke internal combustion engine, resulting in higher performance at high RPM, and lower fuel consumption at low RPM. The VTEC system uses two camshaft profiles and hydraulically selects between profiles. It was invented by Honda engineer Ikuo Kajitani. It is distinctly different from standard VVT systems which change only the valve timings and do not change the camshaft profile or valve lift in any way.
In internal combustion engines, variable valve timing (VVT) is the process of altering the timing of a valve lift event, and is often used to improve performance, fuel economy or emissions. It is increasingly being used in combination with variable valve lift systems. There are many ways in which this can be achieved, ranging from mechanical devices to electro-hydraulic and camless systems. Increasingly strict emissions regulations are causing many automotive manufacturers to use VVT systems.
VVT-i, or Variable Valve Timing with intelligence, is an automobile variable valve timing technology developed by Toyota. The Toyota VVT-i system replaces the Toyota VVT offered starting in 1991 on the 5-valve per cylinder 4A-GE engine. The VVT system is a 2-stage hydraulically controlled cam phasing system.
The LA engines are a family of pushrod OHV small block 90° V-configured gasoline engines built by Chrysler Corporation. It was factory-installed in passenger vehicles, trucks and vans, commercial vehicles, marine and industrial applications from 1964 through 1991 (318) & 1992 (360). The combustion chambers are wedge-shaped, rather than the polyspherical combustion chambers in the predecessor A engine or the hemispherical combustion chambers in the Chrysler Hemi engine. LA engines have the same 4.46 in (113 mm) bore spacing as the A engines. LA engines were made at Chrysler's Mound Road Engine plant in Detroit, Michigan, as well as plants in Canada and Mexico. The "LA" stands for "Light A", as the older "A" engine it was closely based on was nearly 50 pounds heavier. Willem Weertman, who later became Chief Engineer – Engine Design and Development, was in charge of the conversion. The basic design of the LA engine would go unchanged through the development of the "Magnum" upgrade (1992-1993) and into the 2000s with changes to enhance power and efficiency.
An overhead camshaft (OHC) engine is a piston engine where the camshaft is located in the cylinder head above the combustion chamber. This contrasts with earlier overhead valve engines (OHV), where the camshaft is located below the combustion chamber in the engine block.
An overhead valve (OHV) engine is a piston engine whose valves are located in the cylinder head above the combustion chamber. This contrasts with earlier flathead engines, where the valves were located below the combustion chamber in the engine block.
A flathead engine, also known as a sidevalve engine or valve-in-block engine is an internal combustion engine with its poppet valves contained within the engine block, instead of in the cylinder head, as in an overhead valve engine.
A tappet is most commonly a component in an internal combustion engine which converts the rotating motion of the camshaft into linear motion of the valves, either directly or indirectly.
Valve float is an adverse condition which can occur at high engine speeds when the poppet valves in an internal combustion engine valvetrain do not properly follow the closure phase of the cam lobe profile. This reduces engine efficiency and performance. There is also a significant risk of severe engine damage due to valve spring damage, and/or pistons contacting the valves, and/or catastrophic lifter and cam lobe failure, especially with roller lifters.
In a piston engine, the valve timing is the precise timing of the opening and closing of the valves. In an internal combustion engine those are usually poppet valves and in a steam engine they are usually slide valves or piston valves.
In the context of an internal combustion engine, a rocker arm is a valvetrain component that typically transfers the motion of a pushrod to the corresponding intake/exhuast valve.
The cam-in-block valvetrain layout of piston engines is one where the camshaft is placed within the cylinder block, usually beside and slightly above the crankshaft in a straight engine or directly above the crankshaft in the V of a V engine. This contrasts with an overhead camshaft (OHC) design which places the camshafts within the cylinder head and drives the valves directly or through short rocker arms.
A hydraulic tappet, also known as a hydraulic valve lifter or hydraulic lash adjuster, is a device for maintaining zero valve clearance in an internal combustion engine. Conventional solid valve lifters require regular adjusting to maintain a small clearance between the valve and its rocker or cam follower. This space prevents the parts from binding as they expand with the engine's heat, but can also lead to noisy operation and increased wear as the parts rattle against one another until they reach operating temperature. The hydraulic lifter was designed to compensate for this small tolerance, allowing the valve train to operate with zero clearance—leading to quieter operation, longer engine life, and eliminating the need for periodic adjustment of valve clearance.
The intake/inlet over exhaust, or "IOE" engine, known in the US as F-head, is a four-stroke internal combustion engine whose valvetrain comprises OHV inlet valves within the cylinder head and exhaust side-valves within the engine block.