How does firm innovation respond to changing trade environments? This paper investigates this question using the matched administrative datasets for UK firms' R&D expenditures and their trade exposures between 2002 and 2011. I find a strong adverse impact of import competition from China on UK firms' R&D, which is supportive of the `Schumpeterian hypothesis'. There is no evidence that the improved access to Chinese inputs for individual firms offset this negative competition channel. Increased export demand, by contrast, significantly stimulates firms' innovation efforts. Our results also reveal heterogeneity in the R&D responses depending on the firms' initial conditions: First, more productive British firms raise their R&D spending by much more in response to increased foreign demand. Second, exporters reduce R&D by less than non-exporters in the face of the rising Chinese competition. These findings together imply that innovation of purely domestic and less profitable firms was most hurt by globalization, leading to a widening productivity gap across firms.