The Network-on-Chip (NoC) is Network-version of System-on-Chip (SoC) means that on-chip communication is done through packet based networks. In NOC topology, routing algorithm and switching are main terminology .The routing algorithm is one of the key factor in NOC architecture. The routing algorithm, which defines as the path taken by a packet between the source and the destination. As XY routing algorithm mainly used in NOC because of its simplicity. This paper basically review of XY routing algorithm in which we study a different type of XY routing algorithm . The classification of XY routing algorithm is totally depend upon the environment and requirement. Such that IX/Y routing algorithm is for less collision in network ,for deadlock-free and livelock-free DyXY is used, for fault-tolerant XYX routing algorithm is proposed and Adaptive XY routing algorithm is used for fully utilization of network resource.