Recent technological advances have motivated large-scale deployment of RFID systems. However, a number of critical design issues relating to efficient detection of tags remain unresolved. In this paper, we address three important problems associated with tag detection in RFID systems: (i) accurately detecting RFID tags in the presence of reader interference (reader collision avoidance problem); (ii) eliminating redundant tag reports by multiple readers (optimal tag reporting problem); and (iii) minimizing redundant reports from multiple readers by identifying a minimal set of readers that cover all tags present in the system (optimal tag coverage problem). The underlying difficulties associated with these problems arise from the lack of collision detection mechanisms, the potential inability of RFID readers to relay packets generated by other readers, and severe resource constraints on RFID tags. In this paper we present a randomized, distributed and localized Reader Collision Avoidance (RCA) algorithm and provide detailed probabilistic analysis to establish the accuracy and the efficiency of this algorithm. Then, we prove that the optimal tag coverage problem is NP-hard even with global knowledge of reader and tag locations. We develop a distributed and localized Redundant Reader Elimination (RRE) algorithm, that efficiently identifies redundant readers and avoids redundant reporting by multiple readers. In addition to rigorous analysis of performance and accuracy, we provide results from elaborate simulations for a wide range of system parameters, demonstrating the correctness and efficiency of the proposed algorithms under various scenarios.