Matrix metalloproteinases (MMPs) regulate a wide range of biological functions; hence, they have invited great attention for the studies on their structures and functions, and since their overactivation leads to several diseases, the design and discovery of their potent inhibitors have become the need of the day. Since there have been so far discovered 28 different types of human MMPs, the specificity of binding of inhibitors with each different MMP needs special attention. The chapter presents the X-ray crystallographic and NMR studies on three-dimensional structures of a number of MMPs to reveal their catalytic site, subsites, specificity of binding with substrate and inhibitors, and catalytic mechanism. In addition to catalytic site, MMPs possess some subsites designated by unprimed and primed S, e.g., S1, S2, S3 and S1', S2', S3'. Among these, the S1' pocket varies the most among the different MMPs varying in both the amino acid makeup and depth of the pocket (shallow, intermediate, and deep pocket MMPs). This, along with the flexibility in the structures of MMPs, could be of great help in the design and the development of selective MMP inhibitors (MMPIs). The determination of affinity of inhibitors and the cleavage position of peptide substrates is mainly based on P1'-S1' interaction (P1', the group in inhibitor or substrate binding to S1' pocket of the enzyme), and it is the main determinant for the affinity of inhibitors and the cleavage position of peptide substrates.