The present invention features compositions and methods useful in detecting counterfeit products and product diversion. The methods include packaging and indelibly marking products through an opening in their container and/or through a wall of the container that includes a hole therein. Unique identifiers are placed on the product and the container. In other methods, the product is not packaged within a container but is indelibly marked with first and second representations of a unique identifier, either or both of which can be machine-readable, human-readable, and/or at least partially randomized. An apparatus for carrying out the methods of product marking is also disclosed.