Most high-speed IP routers exploit cell-based switching fabrics, whose scalability and performance are mainly affected by queuing scheme and scheduling algorithm. Input-queued router is referred to as an ideal structure in terms of scalability. However, it needs an efficient scheduling algorithm to guarantee throughput and delay. Several input-queued scheduling algorithms are surveyed in this paper. The scheduling algorithms are classified into four classes: maximum size matching, maximum weight matching, stable marriage matching, and deterministic scheduling algorithm. The similarities and the difference of different algorithms in mechanisms of each class are described, and their performances are compared. Finally, the future directions and possible open problems are discussed.