<p>Does inward foreign direct investment (FDI) promote or inhibit the technological innovation of local firms? Prior research has generated mixed views and findings on this important question. To address this puzzle, we propose that FDI spillover and crowding-out effects may apply to different phases of innovation (i.e., idea generation and R&amp;D implementation) respectively, which then leads to differential impacts of FDI on incremental and radical innovation. The results from a panel dataset of Chinese listed firms show that industry-level FDI is positively related to incremental innovation but has an inverted U-shaped impact on radical innovation. Furthermore, we find that technology gap reinforces the positive impact of FDI on incremental innovation while making its inverted U-shaped impact on radical innovation more pronounced, and when FDI local market focus is higher, the inverted U-shaped relationship between FDI and radical innovation is steeper. These findings reconcile the inconsistency regarding how FDI may affect local innovation and provide a novel analysis framework for the FDI literature.</p>