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A Cassegrain reflector telescope is a reflector telescope with two mirrors, a concave primary mirror and convex secondary (as opposed to a Gregorian telescope, which has a concave secondary). The original Cassegrain design, which is still used for many optical telescopes, used a hole in the primary to allow light to pass through to a focal plane behind it. The adjective Cassegrain is now used even if the focal plane is located in front of the primary, and would likely be used even if a flat tertiary mirror were used to place the focal plane to the side (i.e., a fold mirror, analogous to a Newtonian telescope's). Some radio telescopes and other radio antennas use the Cassegrain design, including off-axis telescopes, that have the primary reflector forming a portion of the sphere or paraboloid to one side of the optical axis.
The classical design has a parabolic primary mirror and a hyperbolic convex secondary mirror. The advantage of the Cassegrain design over a simple flat secondary is that the focal length can be set so the secondary mirror is small and blocks little incoming light, even though the focal plane is behind the primary mirror, which can be useful for small amateur telescopes as well as for large telescopes, for handling large instruments. The general Cassegrain design (concave and convex mirrors) is used for various more specific designs, i.e., the terms for telescope types are not mutually-exclusive. An example variant is the Ritchey-Chrétien telescope, which specifies the shapes of the primary and secondary.
Some major research telescopes are set up so they can operate as a Cassegrain telescope for some purposes, and for others, use some other configuration, e.g., as a prime focus telescope. Example research Cassegrain telescopes:
Many more are Ritchey-Chrétien telescopes.