Exchangeability is a key to model network data with Bayesian model. The Aldous-Hoover representation theorem based exchangeable graph model can't generate sparse network, while empirical studies of networks indicate that many real-world complex networks have a power-law degree distribution. Kallenberg representation theorem based exchangeable graph model can admit power-law behavior while retaining desirable exchangeability. This article offers an overview of the emerging literature on concept, theory and methods related to the sparse exchangeable graph model with the Caron-Fox model and the Graphex model as examples. First, developments of random graph models, Bayesian non-parametric mixture models, exchangeability representation theorem, Poisson point process, discrete non-parametric prior etc. are discussed. Next, the Caron-Fox model is introduced. Then, simulation of the sparse exchangeable graph model and related methods such as truncated sampler, and marginalized sampler are summarized. In addition, techniques of model posterior inference are viewed. Finally, state-of-the-art and the prospects for development of the sparse exchangeable graph model are demonstrated.