The fast development of Ad hoc networks in the past few years made it as a key part of the next generation network. This paper introduces various existing routing algorithms including multipath routing algorithmsin Ad hoc networks, such as the table-driven routing protocols and source-initiated on-demand routing algorithms, especially the source-initiated on-demandrouting. For the source-initiated on-demand routing, we analyze the time complexity, communication complexity, etc. Then we further do the investigation on QoS of Ad hoc networks, not only referring to the delay and the bandwidth, but also the stability of the link and routing, also including the power consumption.In the last part, we further introduce our research results on QoS routing algorithms.