When invasive species become integrated within a food web, they may have numerous direct and indirect impacts on the native community by creating novel trophic links, and modifying or disrupting existing ones. Here we discuss these impacts by drawing on examples from freshwater ecosystems, and argue that future research should quantify changes in such trophic interactions (i.e. the links in a food web), rather than simply focusing on traditional measures of diversity or abundance (i.e. the nodes in a food web). We conceptualise the impacts of invaders on trophic links as either direct consumption, indirect trophic effects (e.g. cascading interactions, competition) or indirect nontrophic effects (e.g. behaviour mediated). We then discuss how invader impacts on trophic links are context-dependent, varying with invader traits (e.g. feeding rates), abiotic variables (e.g. temperature, pH) and the traits of the receiving community (e.g. predators or competitors). Co-occurring invasive species and other environmental stressors, such as climate change, will also influence invader impacts on trophic links. Finally, we discuss the available methods to identify new food web interactions following invasion and to quantify how invasive species disrupt existing feeding links. Methods include direct observations in the field, laboratory trials (e.g. to quantify functional responses) and controlled mesocosm experiments to elucidate impacts on food webs. Field studies which use tracer techniques, such as stable isotope analyses, allow diet characterisation of both invaders and interacting native species in the wild. We conclude that invasive species often drastically alter food webs by creating and disrupting trophic links, and future research should be directed particularly towards disentangling the effects of invaders from other environmental stressors.