We study spillovers between REITs and stock markets in a global context. We compute both directional and net spillover indexes in a global and dynamic setting. We use LASSO methods to include many markets in our analysis. Our findings indicate that connectedness between these markets is high. On average three REIT markets and one stock market are net volatility transmitters. Considerable time variation is observed. Spillovers are substantially higher during crises. While stock markets were the main volatility transmitters during the Subprime Financial Crisis, REIT markets have become major volatility transmitters during the last decade. Our results have important implications for global investors.