Computational protein design facilitates the discovery of novel proteins with prescribed structure and functionality. Exciting designs were recently reported using novel data-driven methodologies that can be roughly divided into two categories: evolutionary-based and physics-inspired approaches. The former infer characteristic sequence features shared by sets of evolutionary-related proteins, such as conserved or coevolving positions, and recombine them to generate candidates with similar structure and function. The latter approaches estimate key biochemical properties, such as structure free energy, conformational entropy, or binding affinities using machine learning surrogates, and optimize them to yield improved designs. Here, we review recent progress along both tracks, discuss their strengths and weaknesses, and highlight opportunities for synergistic approaches.