Network data is an important area in modern statistics. Parameter estimation and community detection are two key questions in analyzing network data. In this talk, I will present results in both problems. I will first form the problem of network parameter estimation as nonparametric graphon estimation, and establish its link to nonparametric regression. The minimax rate of graphon estimation consists of two parts: the nonparametric part and the clustering part. An interesting implication is that the smoothness of the graphon does not affect the minimax rate once it is larger than 1. For community detection, I will present a two-step polynomial-time algorithm that can achieve the minimax optimal misclassification rate. The procedure consists of a novel spectral initialization step and a majority voting refinement step. A careful data-splitting idea is the key to link the two steps.