Measures of maximal entropy can characterize the global stability of a system from a measure-theoretic perspective. There is considerable interest in investigating the existence, finiteness, and deep ergodic properties of maximal entropy measures. For non-uniformly hyperbolic diffeomorphisms, advances in this direction have been made by Newhouse, Buzzi, Crovisier, Sarig, and others. In this talk, we present recent progress on measures of maximal entropy for three-dimensional vector fields with singularities.