This chapter offers a selective overview of several structures that generalize the notion of a signed graph. The term ‘generalize’ is used informally to indicate that whenever a matrix associated with a given structure extends or includes the corresponding matrix of a signed graph, we do not insist on strict formal definitions. Because each structure comes with an extensive body of results on its own, the overview is necessarily concise and focuses on presenting the structures rather than detailing their full theoretical developments. In particular, the chapter discusses graphs defined by Hermitian matrices, including weighted graphs, various families of gain graphs, and both mixed and extended mixed graphs, treating each of these topics in meaningful depth.