Over the past forty years, financial markets throughout the world have steadily become more open to foreign investors. With open markets, asset prices are determined globally. A vast literature on portfolio choice and asset pricing has evolved to study the importance of global factors as well as local factors as determinants of portfolio choice and of expected returns on risky assets. There is growing evidence that risk premia are increasingly determined globally. An important outcome of this force of globalization is increased comovement in asset prices across markets. This survey study examines the literature on the dynamics of comovements in asset prices and volatility across markets around the world. The literature began in the 1970s in conjunction with early theoretical developments on international asset pricing models, but it blossomed in the late 1980s and early 1990s with the availability of comprehensive international stock market databases and the development of econometric methodology to model these dynamics.