Resource discovery is an important fundamental aspect and a crucial task in Mobile Peer-to-Peer Networks (MP2P). To compliment network dynamics and churn, the unstructured search architecture is widely used. The key goal of an efficient search scheme is to find the required resource with minimal search latency, low overhead, and low power consumption to better suit the nature of mobile nodes where resource constraints are the major bottleneck. Resource discovery thus becomes an integral part of the distributed architecture and resource sharing systems. In the past, many resource discovery strategies are proposed for Mobile P2P networks. A schematic and tabular classification of these systems enables one to review the existing works under one umbrella. This article presents an overview of such several different schemes for performing resource discovery in the MP2P network broadly classified under six different categories, i.e., centralized, unstructured, structured, super node based, hybrid, and other general lookup schemes. We also give a brief comparison of P2P, MANET, and P2P MANETs. Further, we discuss various routing schemes in such an evolving network. In this survey, we study and review the existing resource discovery techniques in MP2P systems. The classification of each scheme with their advantages and disadvantages are discussed. We highlight a few open research issues, and brief the role of network topology and its structure on the performance of the resource search protocols. Further, we also glimpse on the security threats in MP2P networks and suggest their countermeasures. And, finally, a summary of each method is given, along with their lookup complexities.