The grid computing handles complex applications in a distributed management manner. Resource discovery approach is one of the most important services affecting grid performance. There are many aspects of characteristics of global grids such as dynamicity, scalability, and heterogeneity. The resource discovery approaches face with many challenges such as latency, quality of results, efficiency, reliability, maintenance cost and so on. This paper focuses on introduces the resource discovery approaches used in grid computing environments along with their behaviors in different conditions.