  The rich and varied ways that genetic material can be passed between species
has motivated extensive research into the theory of phylogenetic networks.
Features that align with biological processes, or with mathematical
tractability, have been used to define classes and prove results, with the
ultimate goal of developing the theoretical foundations for network
reconstruction methods. We have now reached the point that a collection of
recent results can be drawn together to make one class of network, the
so-called normal networks, a clear leader. We may be at the cusp of practical
inference with phylogenetic networks.
