This paper examines the effect of the internationalisation of firms via foreign direct investment and trade on their innovation and productivity performance. We use micro data from two waves of the Community Innovation Survey of enterprises in Ireland covering the period 2004-2008 and estimate a structural model to analyse the role of foreign direct investment and exporting in the relationships between innovation investment, innovation output and productivity. Our econometric results suggest that foreign affiliates and domestic exporters are more likely to invest in innovation and, conditional on investing in innovation, they are more likely to have successful innovation output and a higher productivity in comparison to firms that serve only the domestic market. While foreign linkages per se explain to a large extent the unconditional innovation output and productivity differentials, when we control for other factors, we find that the innovation output differential is accounted to a large extent by access to external knowledge flows while the productivity differential is mainly due to the fact that firms with foreign linkages are closer to the technology frontier.