Among proteins of known three-dimensional structure, only a few possess complex topological features such as knotted or interlinked (catenated) protein backbones. Such unusual proteins offer potentially unique insights into folding pathways and stabilization mechanisms. They also present special challenges for both theorists and computational scientists interested in understanding and predicting protein-folding behavior. Here, we review complex topological features in proteins with a focus on recent progress on the identification and characterization of knotted and interlinked protein systems. Also, an approach is described for designing an expanded set of knotted proteins.