Understanding how markets are connected and shocks are transmitted is an important issue for policymakers and market participants. In this paper, we examine the connectedness of Asian equity markets within the region and vis-à-vis other major global markets. Using time-varying connectedness measures, we address the following questions: (1) How has connectedness in asset returns and volatilities changed over time? Do markets become more connected during crises periods? (2) Which markets are major sources and major recipients of shocks? Has there been a shift in terms of the net shock givers and shock receivers (directional connectedness over time)? Finally, we investigate the connectedness between China's equity markets and other countries' equity markets since August 2015 to highlight the growing importance of emerging market economies, particularly China, as sources of shocks.