Publisher Summary Considerable amount of structural data on 3D protein structure has established structure comparison as an essential technique for understanding protein sequence, structure, function, and evolution. The goal is to predict 3D protein structures from amino acid sequence information alone. A major step toward this goal is to determine a method for discovering common protein structures in databases such as the Protein Data Bank, so that a better understanding of protein structure and function can be pieced together. Structure comparison algorithms are used to identify a set of residue equivalencies between two proteins based on their 3D coordinates. This set of equivalencies is called a structure alignment, and it allows the superposition of one protein structure onto the other after rigid rotation and/or translation. Structure alignments can indicate if two proteins share the same fold, or structural unit. Structure alignment is also used as the gold standard for evaluating protein structure prediction methods. This chapter focuses on the application of evolutionary computation to protein structure similarity problems and provides an example of a hybridization of evolutionary algorithms and other optimization techniques. The combination of these approaches offers a new and exciting method for protein structure comparison with increased specificity and sensitivity compared with previous methods.