The multispecies coalescent (MSC) model provides a compelling framework for building phylogenetic trees from multilocus DNA sequence data. The pure MSC is best thought of as a special case of so-called “multispecies network coalescent” models, in which gene flow is allowed among branches of the tree, whereas MSC methods assume there is no gene flow between diverging species. Early implementations of the MSC, such as “parsimony” or “democratic vote” approaches to combining information from multiple gene trees, as well as concatenation, in which DNA sequences from multiple gene trees are combined into a single “supergene,” were quickly shown to be inconsistent in some regions of tree space, in so far as they converged on the incorrect species tree as more gene trees and sequence data were accumulated. The anomaly zone, a region of tree space in which the most frequent gene tree is different from the species tree, is one such region where many so-called “coalescent” methods are inconsistent. Second-generation implementations of the MSC employed Bayesian or likelihood models; these are consistent in all regions of gene tree space, but Bayesian methods in particular are incapable of handling the large phylogenomic data sets currently available. Two-step methods, such as MP-EST and ASTRAL, in which gene trees are first estimated and then combined to estimate an overarching species tree, are currently popular in part because they can handle large phylogenomic data sets. These methods are consistent in the anomaly zone but can sometimes provide inappropriate measures of tree support or apportion error and signal in the data inappropriately. MP-EST in particular employs a likelihood model which can be conveniently manipulated to perform statistical tests of competing species trees, incorporating the likelihood of the collected gene trees on each species tree in a likelihood ratio test. Such tests provide a useful alternative to the multilocus bootstrap, which only indirectly tests the appropriateness of competing species trees. We illustrate these tests and implementations of the MSC with examples and suggest that MSC methods are a useful class of models effectively using information from multiple loci to build phylogenetic trees.