Since finding the nearest point in a lattice for multi-input multi-output (MIMO) channels is NP-hard, simplified algorithms such as sphere decoder (SD) have been proposed. List sphere decoder (LSD), which is a modified version of SD, allows soft information to be extracted for channel decoding and iterative detection/decoding. In this paper, recently proposed efficient methods for reducing the computational complexity of SD and LSD with depth-first tree searching are summarized. Numerous simulations have been carried out and comparison has been made based on the average number of processing cycles. We also present two efficient schemes which can decrease hardware complexity without significant performance degradation, restricted list updating in LSD and restricted node storing at each tree level.