The last couple of decades have witnessed an explosive development in models, theory and algorithms for inferences of network data. Among the many tasks in statistical network analysis, community detection has arguably received the most attention in the literature. However, there are still some gaps in the existing research. For example, most of the literature focuses on the frequentist inference which does not provide an easy path for uncertainty quantification. In addition, a majority of existing work assumes that the number of communities in a network is known which can be restrictive. To address these problems, we propose some Bayesian models for community detection in networks by employing novel random partition priors. Such models allow uncertainty quantification as well as learning the community structure via posterior inference without having to specify a known number of communities a priori. In Chapter two of the thesis, we first propose a Bayesian model for weighted networks by employing the Chinese Restaurant Process (CRP) as a random partition prior for the community structure, under which a weighted stochastic block model is assumed. In Chapter three of the thesis, we then propose a Bayesian model for community detection in a sparse weighted network by combining a random partition prior with a spike and slab type model. More specifically, the sparsity of a weighted network (expressed through the probability of forming a zero edge between two nodes) is explicitly modeled as the spike part of the spike and slab distribution. The weighted network is assumed to follow a mixture of the stochastic block model in which both the sparsity and edge weights play a role in informing the community structure of a network. Efficient MCMC algorithms are developed, and the model and algorithms are applied to extensive simulation studies and real data analysis. The last chapter (Chapter four) of the thesis is devoted to developing efficient algorithms for change point detection in sparse dynamic networks. More specifically, graphon estimators are first obtained, based on which a screening and detection algorithm for detecting change points is proposed. Our model is purely nonparametric which does not rely on specific model assumptions and can effectively utilize the network structure for detecting change points. We provide theoretical guarantees of such algorithms by proving consistency of the detection algorithm. The thesis ends with a summary.