This chapter considers a radar with an antenna consisting of several subapertures, or antenna elements; the echoes received by each subaperture are processed using the adaptive matched filter. Such a radar is capable of a certain degree of suppression of jammers, as well as (for an airborne radar) more effective endoclutter MTI. A single-aperture radar receives a series of echoes, each characterized by the time at which it is received. A multiple-subaperture radar receives a set of echoes, each characterized not only by the reception time but also by the subaperture on which it is received. Because the subapertures are characterized by their location in space, the processing of the combined set of echoes is referred to as space-time processing. If spatial and temporal weights are adaptively calculated (i.e., using the adaptive matched filter), the technique is called space-time adaptive processing (STAP). This discussion of STAP follows that of Ward; Klemm has also developed a detailed exposition. This chapter summarizes the results; more complete derivations of equations can be found. Although the discussion here is in the context of an airborne radar, it can also be applied to a stationary surface-based radar by setting the platform velocity equal to zero. That is particularly applicable to jammer suppression.