Random regular graphs models play an important role in random graph theory and applications, but the models are harder to be investigated than the corresponding Erdos - Renyi models due to the lack of independence between the edges. However the two models share many similar properties. In this talk we will discuss the comparison method, which transform properties of regular graphs into properties of Erdos Renyi ones. Several applications and open problems will be discussed, including our new result on the convergence of empirical spectral distribution of biregular bipartite graphs.