Frame matroids and lifted-graphic matroids are matroids defined using graphs. They are two very important classes of matroids, in part due to their prominent role in the Matroid Minor Project. Recently Geelen, Gerards, and Whittle completed the first formal study of the class of so-called quasi-graphic matroids, which describes a spectrum of matroids contained between frame matroids and lifted-graphic matroids. The three classes of matroids are minor-closed, each of which generalises the class of graphic matroids and exhibits clear graph structure. In this talk, I will introduce some recent results, problems, and conjectures related to the three classes of matroids. No background on matroid theory is required for the audience.