Artery calcification reflects an admixture of factors such as ectopic osteochondral differentiation with primary host pathological conditions. We review how genetic factors, as identified by human genome-wide association studies, and incomplete correlations with various mouse studies, including knockout and strain analyses, fit into "pieces of the puzzle" in intimal calcification in human atherosclerosis, and artery tunica media calcification in aging, diabetes mellitus, and chronic kidney disease. We also describe in sharp contrast how ENPP1, CD73, and ABCC6 serve as "cogs in a wheel" of arterial calcification. Specifically, each is a minor component in the function of a much larger network of factors that exert balanced effects to promote and suppress arterial calcification. For the network to normally suppress spontaneous arterial calcification, the "cogs" ENPP1, CD73, and ABCC6 must be present and in working order. Monogenic ENPP1, CD73, and ABCC6 deficiencies each drive a molecular pathophysiology of closely related but phenotypically different diseases (generalized arterial calcification of infancy (GACI), pseudoxanthoma elasticum (PXE) and arterial calcification caused by CD73 deficiency (ACDC)), in which premature onset arterial calcification is a prominent but not the sole feature.