We investigate the connectedness of the most significant global equity indices that comprise companies with the highest environmental, social, and governance (ESG) performance. Motivated by the rapid growth of socially responsible investing during the last two decades, we examine whether these investments are prone to similar exogenous economic and financial shocks as their conventional counterparts. Employing a variety of influential macroeconomic and financial variables over the period 10/1/2007–4/15/2020, we document statistically significant and consistent transmissions between the employed equity indices throughout the sample period. In particular, the connectedness exhibits dynamic patterns during three periods: the European sovereign debt crisis, the systemic Greek problems, and the outbreak of the coronavirus pandemic. We also find that developed equity markets are the shock transmitters to Asian and other emerging markets. Our results highlight the risk of contagion and the diminishing portfolio diversification benefits of these equity indices during turbulent periods.