This work is a survey of the average cost control problem for discrete-time Markov processes. We have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades. Our exposition ranges from finite to Borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies. We have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography. We have also identified several important questions which are still left open to investigation.