International diversification has costs and benefits, depending on the degree of asset dependence. We study international diversification with two dependence measures: correlations and extreme dependence. We discover that dependence has typically increased over time, and document mixed evidence on heavy tails in individual countries. Moreover, we uncover three additional findings related to dependence. First, the timing of downside risk differs depending on the region. Surprisingly, recent Latin American returns exhibit little downside risk. Second, Latin America exhibits a great deal of correlation complexity. Third, according to the empirical results, correlation does not vary with returns, but extreme dependence does vary monotonically with regional returns. Our results are consistent with a tradeoff between international diversification and systemic risk. They also suggest international limits to diversification, and that international investors demand some compensation for joint downside risk during extreme events.