Early evolutionary thinkers proposed relatively simple models to describe processes of evolution, and these are the basis of evolutionary models still used today. Recent research has since shown that evolutionary relationships among plants can be complex and difficult to reconstruct even from molecular data. In plants there is a continuum of processes, ranging from reticulate relationships within a sexually reproducing population, incomplete lineage sorting and hybridization between recently diverged species, allopolyploidy between more distantly related species, to symbioses and endosymbiosis. These aspects of plant biology can create practical problems for interpreting bifurcating gene trees and identifying species. The promise of “omics” is that it will provide data and analyses to improve our understanding of the nature of species and their phylogenetic relationships. We highlight the importance of distinguishing evolutionary processes and evolutionary models, and stress that improving the understanding of micro-evolutionary processes is necessary to inform current debate on whether or not to accept paraphyletic species.