Species-level phylogenetic inference under the multispecies coalescent model remains challenging in the typical inference frameworks (e.g., the likelihood and Bayesian frameworks) due to the dimensionality of the space of both gene trees and species trees. Algebraic approaches intended to establish identifiability of species tree parameters have suggested computationally efficient inference procedures that have been widely used by empiricists and that have good theoretical properties, such as statistical consistency. However, such approaches are less powerful than approaches based on the full likelihood. Methods based on composite likelihood are a compromise between these two approaches that enable computationally efficient inference while maximizing use of the available sequence data. In this talk, I’ll describe the relationship between these two approaches, highlighting the strengths and weaknesses of each and providing directions for future work.