This paper provides cross-country firm-level evidence on productivity spillovers from foreign direct investment (FDI), separately for greenfield FDI and cross-border mergers and acquisitions (M&As). The granularity of bilateral sector-level FDI datasets allows for addressing possible endogeneity issues by applying a two-step approach whereby an exogenous FDI measure is constructed from a gravity-type regression of bilateral FDI flows. When looking at the effects of greenfield investments on firm labor productivity we find: i) positive intra-industry spillover effects for firms located in advanced countries, and ii) positive backward spillover effects for firms located in emerging and developing countries. These spillovers are driven entirely by FDI from advanced countries. The results from cross-border M&As are noisier, with weakly suggestive evidence for positive intra-industry spillovers in advanced countries but negative backward spillovers in emerging markets and developing countries.