This paper explores R&D offshoring's role in radical product innovations. These innovations are important for companies' growth strategies, and we check the extent to which companies rely on external sources, which may bring knowledge that differs significantly from that already present internally. The evidence for Spanish firms between 2004 and 2013 shows that R&D offshoring influences significantly the intensity of radical but not of incremental innovations. This influence is apparently smaller when external knowledge comes from universities or research institutions rather than from the business sector. The recent financial crisis also exerted a detrimental effect on this influence, as compared with the previous period of economic growth.