It is well-known that regime switching models are able to capture the presence of rich non-linear patterns in the joint distribution of asset returns. After reviewing key concepts and technical issues related to specifying, estimating, and using multivariate Markov switching models in financial applications, in this paper we map the presence of regimes in means, variances, and covariances of asset returns into explicit dynamics of the Markowitz mean-variance frontier. In particular, we show both theoretically and through an application to international equity portfolio diversification that substantial differences exist between bull and bear, regime-specific frontiers, both in statistical and in economic terms. Using Morgan Stanley Capital International (MSCI) investable indices, we characterize mean-variance frontiers and optimal portfolio strategies in bull periods, in bear periods, and in periods where high uncertainty exists on the nature of the current regime.