Since the 1970s, after the seminal work of Rossmann and Argos (1978) comparing binding sites of known enzyme structures, the comparison and alignment of protein structures has come to be a fundamental and widely used task in computational structure biology. Three main steps are needed for comparing two protein structures: first, the detection of their common similarities; second, the alignment of the structures based on such similarities; and third, a statistical measure of the similarity. Considering the first two steps, structure comparison refers to the analysis of the similarities and differences between two or more structures, and structure alignment refers to establishing which amino acid residues are equivalent between them. The majority of commonly used methods do a reasonably good job in recognizing obvious similarities between protein structures. However, the alignment of two or more structures is a more difficult task, and its accuracy may depend on the method or program used as well as what the user is trying to accomplish, which will be discussed subsequently. All programs that are briefly described in this chapter perform both steps and are commonly known as protein structure alignment methods.It is also important to immediately clear up any confusion between structure alignment and structure superposition since such terms are often interchanged in the literature. As mentioned above, structure alignment tries to identify the equivalences between pairs of amino acid residues from the structures to superpose, while structure superposition requires the previous knowledge of such equivalences. Thus, structure superposition tries to solve the simpler geometrical task of minimizing the distance between already known equivalent residues of the superimposed structures by finding a transformation that produces either the lowest root-mean-square deviation (RMSD) or the maximal equivalences within an