Hybridization among eukaryotic organisms gives rise to reticulate evolutionary histories, and subsequent potential introgression results in genome mosaics. Consequently, phylogenetic networks have been introduced to model reticulate evolutionary histories. In this talk, I will present our recent work on modeling the evolution of genes and genomes within the branches of phylogenetic networks and the methods we have developed for their inference. Further, I will describe a new comparative genomic method that combines phylogenetic networks with hidden Markov models in order to detect genomic regions with signatures of introgression.