To comprehensively investigate information transmission and risk contagion among global environmental, social, and governance (ESG) stock markets, this paper employs the TVP-VAR time and frequency connectedness approaches to analyze return and volatility connectedness across global ESG stock indexes. The dataset comprises the eleven ESG stock indexes, including both developed and developing markets, spanning from October 1, 2007 to December 31, 2021. We find a strong connectedness between these ESG stock indexes in terms of return and volatility, with the ESG stock indexes in Europe and North America exhibiting mainly outward spillovers and those in Asia Pacific and India displaying mainly inward spillovers. Moreover, return connectedness is concentrated at high frequency, while volatility connectedness is concentrated at low frequency. Both return and volatility connectedness are affected by extreme events, especially the COVID-19 pandemic. However, volatility connectedness changes more dramatically than return connectedness during the pandemic. In addition, high ESG attention leads to low return connectedness but high volatility connectedness. During the pandemic, ESG attention positively affects both return and volatility connectedness across ESG stock indexes. Lastly, portfolios with the minimum time-frequency domain return connectedness exhibit higher hedging effectiveness, while portfolios with the minimum time-frequency domain volatility connectedness generate higher cumulative returns. Overall, this paper enriches the empirical framework for ESG stock markets, provides a reference for investors to invest in the market, and helps regulators to formulate forward-looking regulations that promote financial stability.