The issue of how a newly synthesized polypeptide chain folds to form a protein with a unique three-dimensional structure, otherwise known as the 'protein-folding problem', remains a fundamental question in the life sciences. Over the last few decades, much information has been gathered about the mechanisms by which proteins fold. However, despite the vast topological diversity observed in biological structures, it was thought improbable, if not impossible, that a polypeptide chain could 'knot' itself to form a functional protein. Nevertheless, such knotted structures have since been identified, raising questions about how such complex topologies can arise during folding. Their formation does not fit any current folding models or mechanisms, and therefore represents an important piece of the protein-folding puzzle. This article reviews the progress made towards discovering how nature codes for, and contends with, knots during protein folding, and examines the insights gained from both experimental and computational studies. Mechanisms to account for the formation of knotted structures that were previously thought unfeasible, and their implications for protein folding, are also discussed.