A reflecting telescope uses mirrors to focus the incoming light rays.
Different telescope designs are adopted for convenience and economy or for special purposes.
The simplest design is called the prime focus. In such a design, the detector lies in front of the mirror. The advantage of a prime focus system is that it requires a minumum number of reflections; on the other hand, some of the incoming light rays are blocked. If the mirror is large enough, the fact that the detector lies in front and therefore blocks some of the incoming rays doesn't matter that much in terms of losing light, but some distortion may occur because of diffraction or scattering off the blocking structure.
A Newtonian reflector is common in small telescopes. In this case, a small mirror reflects the light off to the side of the telescope tube.
A Cassegrain design, using a subreflector to reflect the light back through a hole in the primary mirror, is very common in research telescopes. In this case, the detector(s) can be placed behind the mirror, in a convenient location for making adjustments, etc.
A Schmidt telescope uses both a mirror and a correcting lens to produce a perfect image over a wide field.