Grid technologies enable the sharing of a wide variety of distributed resources. To utilize these resources, effective Resource Management systems are needed. Resource Management system performs resource discovery to obtain information about the available resources. However, the complex and dynamic nature of grid resources make sharing and discovery, a challenging issue. Resource Discovery is initiated by a network application to find suitable resources with in the Grid. Resource Discovery process is critical for efficient resource allocation and management. For making the Resource Discovery more efficient and reliable large numbers of Approaches are there. This paper analyses some of existing Approaches for Resource Discovery, which can search for the preferred resources quickly and efficiently (return the correct results quickly and reduce network complexity) in Grid computing. Finally a qualitative comparison between these Approaches based on the factors that affect Grid Resource Discovery process, has been done and results are presented.