Multiple-input multiple-output (MIMO) systems entered most major standards in the past decades, including IEEE 802.11n (Wi-Fi) and long-term evolution (LTE). Moreover, MIMO techniques will be used for 5G by increasing the number of antennas at the base station end. MIMO systems enable spatial multiplexing, which has the potential of increasing the capacity of the communication channel linearly with the minimum of the number of antennas installed at both sides without sacrificing any additional bandwidth or power. To handle the space-division multiplexing (SDM), receivers have to implement new algorithms to exploit the spatial information in order to distinguish the transmitted data streams. This chapter provides an overview of the most well-known and promising MIMO detectors, as well as some unusual-yet-interesting ones. We focus on the description of the different paradigms to highlight the different approaches that have been studied. For each paradigm, we describe the mathematical framework and give the underlying philosophy. When hardware implementations are available in the literature, we provide the results reported and give the according references.