We review the basic features of transition radiation and how they are used for the design of modern Transition Radiation Detectors (TRD). The discussion will include the various realizations of radiators as well as a discussion of the detection media and aspects of detector construction. With regard to particle identification we assess the different methods for efficient discrimination of different particles and outline the methods for the quantification of this property. Since a number of comprehensive reviews already exist, we predominantly focus on the detectors currently operated at the LHC. To a lesser extent we also cover some other TRDs, which are planned or are currently being operated in balloon or space-borne astro-particle physics experiments.

37 pages, 33 figures; review article to appear in Nucl. Instr. Meth. A; links to references, as well as a simulation code (used to produce Figs 5-10), available at http://www-linux.gsi.de/~andronic/physics/trds.html