Introgression and hybridization are important processes in plant evolution, but they are difficult to study from a phylogenetic perspective, because they conflict with the bifurcating evolutionary history typically depicted in phylogenetic models. The role of hybridization in plant evolution is best documented in the form of allo-polyploidizations. In contrast, homoploid hybridization and introgression are less explored, although they may be crucial in adaptive radiations. Here we employ genome-wide data (ddRAD-seq, transcriptomes) to investigate the evolutionary history of Nepenthes, a radiation of c. 160 species of iconic carnivorous plants mainly from tropical Asia. Our data indicates that the main radiation is only c. 5 million years old, and confirms previous bifurcating phylogenies. However, due to a greatly expanded number of loci, we were able test for the first time the long-standing hypotheses of introgression and historical hybridization. The genus presents one very clear case of organellar capture between two distantly related but sympatric groups. Furthermore, all Nepenthes species show introgression signals in their nuclear genomes, as uncovered by a general survey of ABBA-BABA-like statistics. The ancestor of the rapid main radiation shows ancestry from two deeply diverged lineages, as indicated by phylogenetic network analyses. All major clades of the main radiation show further introgression both within and between each other, as suggested by admixture graphs. Our study supports the hypothesis that rapid adaptive radiations are hotspots of introgression in the tree of life, and highlights the need to consider non-treelike processes in evolutionary studies of Nepenthes in particular.