Tropical algebraic geometry studies varieties by `tropicalizing' them into polyhedral complexes. The hope, which is realized surprisingly often, is that difficult algebro-geometric questions will reduce to simpler polyhedral questions. The resulting questions are usually not easy, and that’s good news for us: they have led to several new and interesting research directions in geometric combinatorics. Matroids often play a fundamental role because they are equivalent to tropical linear spaces. This talk will survey a few central aspects of the interplay between matroids and tropical geometry, and discuss some recent developments.