This chapter is a brief review of several traditional STAP schemes as well as an explanation of the complex detection environments in which many radar signal processors must operate. A review of the deterioration of the performance of algorithms, as well as the benefits and drawbacks of newly proposed adaptive processing approaches, has been provided. The chapter discusses that an engineering trade off exists between the design of the algorithm and its computational difficulties in real-world implementation. In the future, we look forward to the potential marriage of several of the presented signal processing techniques to provide overall system robustness and real-time target detection in real-world, non-ideal detection environments.