A procedure commonly used to construct solutions to Maxwell's equations is to introduce a potential which itself satisfies a vector or scalar wave equation. In this connection there are three basic mathematical questions. 1) What class of initial data for the problem can be represented by a particular potential? 2) What is the precise relationship of the one-parameter group delivering solutions to the Cauchy problem for Maxwell's equations to the Cauchy problem for the wave equation that the particular potential satisfies? 3) What is the exact relation of various potentials to one another?