With the increasing demands on high data rate, there has been growing interests in multi-input multi-output (MIMO) technology based on spatial multiplexing (SM) since it can transmit independent information in each spatial stream. Recent standards such as 3GPP LTE-advanced and IEEE 802.11ac support up to eight spatial streams, and massive MIMO and mm-wave systems that are expected to be included in beyond 4G systems are considering employment of tens to hundreds of antennas. Since the complexity of the optimum maximum likelihood based detection method increases exponentially with the number of antennas, low-complexity SM MIMO detection becomes more critical as the number of antenna increases. In this paper, we first review the results on the detection schemes for SM MIMO systems. In addition, massive MIMO reception schemes based on simple linear filtering which does not require exponential increment of complexity will be explained, followed by brief description on receiver design for future high dimensional SM MIMO systems.