After the first unequivocal demonstration of spin transport in graphene, surprisingly working at room temperature (Tombros et al., 2007), it was quickly realised the relevance of this then recently discovered material, for both fundamental spintronics and future applications. Over the last decade, exciting results have made the field of graphene spintronics to blossom and evolve to a next generation of studies extending to new two-dimensional (2D) compounds. This Colloquium reviews recent theoretical and experimental advances in studies of electronic spin transport in graphene and related 2D materials, focusing on the new perspectives provided by heterostructures thereof and their emergent phenomena, including proximity-enabled spin-orbit effects, coupling spin to light, electrical tunability and 2D magnetism. We conclude by listing current challenges and promising research directions.