Designing proteins with tailored structures and functions is a long-standing goal in bioengineering. Recently, deep learning advances have enabled protein structure prediction at near-experimental accuracy, which has catalyzed progress in protein design as well. We review recent studies that use structure-prediction neural networks to design proteins, via approaches such as activation maximization, inpainting, or denoising diffusion. These methods have led to major improvements over previous methods in wet-lab success rates for designing protein binders, metalloproteins, enzymes, and oligomeric assemblies. These results show that structure-prediction models are a powerful foundation for developing protein-design tools and suggest that continued improvement of their accuracy and generality will be key to unlocking the full potential of protein design.