The stunning diversity of molecular functions performed by naturally evolved proteins is made possible by their finely tuned three-dimensional structures, which are in turn determined by their genetically encoded amino acid sequences. A predictive understanding of the relationship between amino acid sequence and protein structure would therefore open up new avenues, both for the prediction of function from genome sequence data and also for the rational engineering of novel protein functions through the design of amino acid sequences with specific structures. The past decade has seen dramatic improvements in our ability to predict and design the three-dimensional structures of proteins, with potentially far-reaching implications for medicine and our understanding of biology. New machine-learning algorithms have been developed that analyse the patterns of correlated mutations in protein families, to predict structurally interacting residues from sequence information alone 1,2. Improved protein energy functions 3,4 have for the first time made it possible to start with an approximate structure prediction model and move it closer to the experimentally determined structure by an energy-guided refinement process 5,6. Advances in protein conformational sampling and sequence optimization have permitted the design of novel protein structures and complexes 7,8 , some of which show promise as therapeutics 9. These advances in protein structure prediction and design have been fuelled by technological breakthroughs as well as by a rapid growth in biological databases. Protein-modelling algorithms (Box 1) are computationally demanding both to develop and to apply. The rapid increase in computing power available to researchers (both CPU-based and, increasingly, GPU-based computing power) facilitates rapid benchmarking of new algorithms and enables their application to larger molecules and molecular assemblies. At the same time, next-generation sequencing has fuelled a dramatic increase in protein sequence databases as genomic and metagenomic sequencing efforts have expanded 10. Advances in software and automation have increased the pace of experimental structure determination, speeding the growth of the database of experimentally determined protein structures (the Protein Data Bank (PDB)) 11 , which now contains close to 150,000 macromolecular structures. Deep-learning algorithms 12 that have revolutionized image processing and speech recognition are now being adopted by protein modellers seeking to take advantage of these expanded sequence and structural databases. In this Review, we highlight a selection of recent breakthroughs that these technological advances have enabled. We describe current approaches to the prediction and design of protein structures, focusing primarily on template-free methods that do not require an