"Identity criteria are powerful tools for the metaphysician. They tell us when items are identical or distinct. Some varieties of identity criteria also try to explain in virtue of what items are identical or distinct. This Element has two objectives: to discuss formulations of identity criteria and to take a closer look at one notorious criterion of object identity, Leibniz's Law. The first section concerns the form of identity criteria. The second section concerns the better-regarded half of Leibniz's Law, the indiscernibility of identicals. The third section turns to the more controversial half of Leibniz's Law, the identity of indiscernibles. The author considers alternatives to Leibniz's Law as well as the possibility that there are no adequate identity criteria to be found"--