Emerging market (EM) assets have historically been regarded as inherently risky and particularly vulnerable to international shocks that result in a general increase in investor risk perceptions. In this paper, we assess the ongoing relevance of this view by examining the linkages between EM and non-EM stock and bond markets in the past two decades, with a focus on how these relationships played out during the global financial crisis of 2007-2009. We evaluate how these linkages have evolved over the period 1992-2009, through statistical tests of whether the volatility of EM financial markets changed - either in their response to international shocks originating in advanced economy markets or in their independent fluctuations. We find that over the longer period EM bond and stock prices have on average moved in the same direction as the prices of non-EM risky assets, and this co-movement has persisted. However, these relationships have evolved somewhat over time. Both EM sensitivity to international shocks and EM-specific volatility in EM sovereign bond spreads appear to have decreased over time, consistent with the greater fundamental stability of EM economies and perhaps a reduced inclination by investors to sell off EM assets in response to a rise in risk perceptions. Somewhat in contrast, while an upward trend in co-variation between EM and non-EM stock prices suggests an increasing degree of global market integration, idiosyncratic volatility has declined, consistent with a diminished level of locally-driven risk in these markets. In addition, the response of EM asset prices to the latest financial crisis appears to be moderate in comparison to historical experience. This evidence may reflect reduced EM vulnerability to external shocks in general, which is consistent with some encouraging improvements in the underlying fundamentals of EM economies over the decade preceding the onset of the crisis.