The explosive growth of mobile intelligent devices has given birth to the emerging data sensing mode of Mobile crowd sensing (MCS), which mainly relies on the mobile intelligent devices and group intelligence to collect the information of the surrounding environment. Compared with traditional sensor networks, MCS is more suitable for large-scale and real-time sensing scenario due to its low cost, high efficiency. Task allocation is a crucial issue in MCS systems which is intended to achieve a good tradeoff between task quality and task cost. It matches the sensing task with the task participation group, which determines the efficiency of the whole system. In this paper, we introduce the influencing factors, optimization objectives, classification and common implementation algorithms of task allocation model in MCS system. Finally, we summarize challenging issues and prospect the future research direction in this area.