Multi-Way Block Models is a set of models proposed to find block structure of interaction with latent memberships for two groups of subjects. Generalized from the Mixed Membership Stochastic Block Models, we investigate the model in multi-ways, as extensions in model settings allowing for different distributions of interaction, and model implementations as variational Bayesian, collapsed Gibbs sampling, collapsed variational Bayesian, and expectation propagation approaches. In this talk, we first overview the model background by a scenario of block structure extracted from network among subjects. Then we discuss the four model implementations with algorithm frames. Finally we demonstrate the model application by comparative simulation studies and real data analysis.