Structural estimation of matching games with transferable utility, including matching games of trading networks and many-to-many matching, is increasingly popular in empirical work. I explore several modeling decisions that need to be made when specifying a structural model for a matching game. One decision is the choice of a game theoretic solution concept to impose in the structural model. I discuss pairwise stability, competitive equilibrium, and noncooperative games such as auctions. Another decision is whether to work with a continuum of agents or a finite number of agents. I explore other issues as well.