RNA-binding proteins (RBPs) are typically thought of as proteins that bind RNA through one or multiple globular RNA-binding domains (RBDs) and change the fate or function of the bound RNAs. Several hundred such RBPs have been discovered and investigated over the years. Recent proteome-wide studies have more than doubled the number of proteins implicated in RNA binding and uncovered hundreds of additional RBPs lacking conventional RBDs. In this Review, we discuss these new RBPs and the emerging understanding of their unexpected modes of RNA binding, which can be mediated by intrinsically disordered regions, protein-protein interaction interfaces and enzymatic cores, among others. We also discuss the RNA targets and molecular and cellular functions of the new RBPs, as well as the possibility that some RBPs may be regulated by RNA rather than regulate RNA.