This paper examines the diversity of the types of links of firms to science and their effect on innovation performance for a sample of Belgian firms. While at the industry level links to science are highly related to the R&D intensity of the sector, we show that there exists considerable heterogeneity in the type of links to science at the firm level. Overall, firms with a science link enjoy superior innovation performance, in particular with respect to innovations that are new to the market. At the invention level, our findings confirm that patents from firms engaged in science are more frequently cited and have a broader technological and geographical impact, but we show that it is crucial to distinguish between direct science links at the invention level and indirect science links at the firm level to encounter these distinct positive effects of science links.