MTI (Moving Target Indication) radar systems have been built for many years, based on sys-tem concepts evolved in the early 1950's. Digital techniques now permit easier implementation, but do not change the basic concepts; staggered repetition periods to eliminate blind speeds; and MTI cancellers with the velocity response shaped by feed forward and feedback techniques. Many pf the existing systems are very successful, even though their performance, measured in terms of MTI improvement factor or subclutter visibility, often falls far short of the performance predicted from linear theory. The basic MTI concepts and definitions are presented, and the real problems of modern surface-based MTI radar systems are discussed. Future signal-processing techniques are postulated.