It is becoming increasingly clear that the evolution of certain organisms (e.g. plants, viruses, bacteria) is not always best represented by a binary leaf-labelled tree. This is due to underlying evolutionary processes such as horizontal gene transfer, recombination and hybridization. Phylogenetic networks provide a framework for exploring and visualizing the complex patterns that can arise from such processes. In this talk we review the split decomposition method for phylogenetic network construction, and discuss some new directions such as NeighborNet and species networks.