Deep generative models that learn from the distribution of natural protein sequences and structures may enable the design of new proteins with valuable functions. While the majority of today's models focus on generating either sequences or structures, emerging co-generation methods promise more accurate and controllable protein design, ideally achieved by modeling both modalities simultaneously. Here we review recent advances in deep generative models for protein design, with a particular focus on sequence-structure co-generation methods. We describe the key methodological and evaluation principles underlying these methods, highlight recent advances from the literature, and discuss opportunities for continued development of sequence-structure co-generation approaches.