A mobile ad-hoc network (MANET) is basically called as a network without any central administration or fixed infrastructure. It consists of a number of mobile nodes that use to send data packets through a wireless medium. There is always a need of a good routing protocol in order to establish the connection between mobile nodes since they possess the property of dynamic changing topology. Further, in all the existing routing protocols, mobility of a node has always been one of the important characteristics in determining the overall performance of the ad hoc network. Thus, it is essential to know about various mobility models and their effect on the routing protocols. In this paper, we have made an attempt to compare different mobility models and provide an overview of their current research status. The main focus is on Random Mobility Models and Group Mobility Models. Firstly, we present a survey of the characteristics, drawbacks and research challenges of mobility modeling. At the last we present simulation results that illustrate the importance of choosing a mobility model in the simulation of an ad hoc network protocol. Also, we illustrate how the performance results of an ad hoc network protocol drastically change as a result of changing the mobility model simulated.