Range shifts can rapidly create new areas of geographic overlap between formerly allopatric taxa and evidence is accumulating that this can affect species persistence. We review the emerging literature on the short- and long-term consequences of these geographic range shifts. Specifically, we focus on the evolutionary consequences of novel species interactions in newly created sympatric areas by describing the potential (i) short-term processes acting on reproductive barriers between species and (ii) long-term consequences of range shifts on the stability of hybrid zones, introgression and ultimately speciation and extinction rates. Subsequently, we (iii) review the empirical literature on insects to evaluate which processes have been studied, and (iv) outline some areas that deserve increased attention in the future, namely the genomics of hybridisation and introgression, our ability to forecast range shifts and the impending threat from insect vectors and pests on biodiversity, human health and crop production. Our review shows that species interactions in de novo sympatric areas can be manifold, sometimes increasing and sometimes decreasing species diversity. A key issue that emerges is that climate-induced hybridisations in insects are much more widespread than anticipated and that rising temperatures and increased anthropogenic disturbances are accelerating the process of species mixing. The existing evidence only shows the tip of the iceberg and we are likely to see many more cases of species mixing following range shifts in the near future.