We introduce finite mixtures of Ising models as a novel approach to study multivariate patterns of associations of binary variables. Our proposed models combine the strengths of Ising models and multivariate Bernoulli mixture models. We examine conditions required for the identifiability of Ising mixture models, and develop a Bayesian framework for fitting them. Through simulation experiments and real data examples, we show that Ising mixture models lead to meaningful results for sparse binary contingency tables.