Multiple-input-multiple-output (MIMO) detection is a problem frequently encountered in digital communications; e.g., detection (or decoding) of spatially multiplexed or space-time coded data in multi-antenna communications, and detection of multiuser signals in CDMA systems (AKA multiuser detection). Even the problem of detecting single-user data sequence in ISI channels back in 70's may be viewed as a MIMO problem, from a more modern perspective. This talk considers maximum-likelihood (ML) MIMO detection, an approach that offers attractive symbol error performance, but often leads to very challenging implementations from an optimization viewpoint. Our emphasis is placed on semidefinite relaxation (SDR), a high-performance efficient method for handling ML MIMO. The idea is to use convex optimization to provide an accurate approximation to the ML MIMO detection problem. The talk will discuss basic concepts and aspects of SDR, provide some insights into why SDR can offer quasi-ML performa nce, and describe the recent trend of its development. The focus of the talk is SDR MIMO detection, but in the process we will also briefly review various MIMO detection techniques.