Pressure relief valve is one of the most important type of safety valves.

This type of valves sets a limit on the rise of pressure within a hydraulic line. In normal operation the valve is closed and no fluid passes through. But if the pressure in the line exceeds the limit the valve opens to relieve the pressure. This protects expensive machinery such as motors, pumps and actuators from becoming damaged from high pressure.

Without a relief valve the pressure can continue to grow until another component fails and pressure is released.

Two Types of Pressure Relief Valves are there.

Direct Acting:
A direct-acting valve may consist of a poppet or ball, held exposed to system pressure on one side and opposed by a spring of pre-set force on the other. This pre-set force is commonly achieved with an adjusting screw acting on the spring. By turning the screw in or out, the operator compresses or decompresses the spring respectively. The valve can be set to open at any pressure within a desired range.
In a normally closed relief valve, the force exerted by the compression spring exceeds the force exerted by system pressure acting on the ball or poppet. The spring holds the ball or poppet tightly seated.
When system pressure begins to exceed the setting of the valve spring, the fluid pushes the ball or poppet, allowing a controlled amount of fluid to bypass to the reservoir, maintaining system pressure at the valve setting. The spring re-seats the ball or poppet when enough fluid is released to drop system pressure below the setting of the valve spring.

The pressure at which a relief valve first opens to allow fluid to flow through is known as cracking pressure. When the valve is bypassing its full rated flow, it is in a state of full-flow pressure. The difference between full-flow and cracking pressure is sometimes known as pressure differential, also known as pressure override.
These valves are generally used for small flows. They don’t leak below cracking pressure and respond rapidly, making them ideal for relieving shock pressures.

The differential between cracking and full open pressure on direct acting relief valves is high. For this reason, they are not recommended for precise pressure control.

Pilot Operated:
The pressure is supplied from the upstream side (the system being protected) to the dome often by a small pilot tube. The downstream side is the pipe or open air where the valve directs its exhaust. The outlet pipe is typically larger than the inlet.
The upstream pressure tries to push the piston open but it is opposed by that same pressure because the pressure is routed around to the dome above the piston. The area of the piston on which fluid force is acting is larger in the dome than it is on the upstream side; the result is a larger force on the dome side than the upstream side. This produces a net sealing force.
The pressure from the pilot tube to the dome is routed through the actual control pilot valve.
The pressure at which the control pilot relieves at is the functional set pressure of the relief valve. When the pilot valve reaches set pressure it opens and releases the pressure from the dome. The piston is then free to open and the main valve exhausts the system fluid.
The control pilot opens either to the main valve exhaust pipe or to atmosphere.
The pilot is designed to open gradually, so that less of the system fluid is lost during each relief event. The piston lifts in proportion to the over-pressure. Blowdown is typically short.
This figure shows a Comparison of action of relief valves at cracking and full flow pressure.
Because pilot operated relief valves do not start opening until the system reaches 90% of full pressure, less fluid is released.
These valves are best suited for high-pressure, high-volume applications. Although their operation is slower than that of direct-acting relief valves, pilot-operated relief valves maintain a system at a more constant pressure while relieving.