The lysyl oxidase family comprises five members in mammals, lysyl oxidase (LOX) and four lysyl oxidase like proteins (LOXL1-4). They are copper amine oxidases with a highly conserved catalytic domain, a lysine tyrosylquinone cofactor, and a conserved copper-binding site. They catalyze the first step of the covalent cross-linking of the extracellular matrix (ECM) proteins collagens and elastin, which contribute to ECM stiffness and mechanical properties. The role of LOX and LOXL2 in fibrosis, tumorigenesis, and metastasis, including changes in their expression level and their regulation of cell signaling pathways, have been extensively reviewed, and both enzymes have been identified as therapeutic targets. We review here the molecular features and three-dimensional structure/models of LOX and LOXLs, their role in ECM cross-linking, and the regulation of their cross-linking activity by ECM proteins, proteoglycans, and by inhibitors. We also make an overview of the major ECM cross-links, because they are the ultimate molecular readouts of LOX/LOXL activity in tissues. The recent 3D model of LOX, which recapitulates its known structural and biochemical features, will be useful to decipher the molecular mechanisms of LOX interaction with its various substrates, and to design substrate-specific inhibitors, which are potential antifibrotic and antitumor drugs.