The evolutionary history of a set of taxa is usually represented by a phylogenetic tree, and this model has greatly facilitated the discus-sion and testing of hypotheses. However, it is well known that more complex evolutionary scenarios are poorly described by such models. Further, even when evolution proceeds in a tree-like manner, analysis of the data may not be best served by using methods that enforce a tree structure, but rather by a richer visualization of the data to evaluate its properties, at least as an essential first step. Thus, phylogenetic net-works should be employed when reticulate events such as hybridization, horizontal gene transfer, recombination, or gene duplication and-loss are believed to be involved, and, even in the absence of such events, phylogenetic networks have a useful role to play. This paper reviews the terminology used for phylogenetic networks and covers both split networks and reticulate networks, how they are defined and how they can be interpreted. Additionally, the paper outlines the beginnings of a comprehensive statistical framework for applying split network meth-ods. We show how split networks can represent confidence sets of trees and introduce a conservative statistical test for whether the conflicting signal in a network is treelike. Finally, this paper describes a new pro-gram SplitsTree4, an interactive and comprehensive tool for inferring different types of phylogenetic networks from sequences, distances and trees.