This thesis deals with the simulation and control of time-dependent, but time-periodic eddy current problems in unbounded domains in $\mathbb{R}^3$. In order to discretize such problems in the full space-time cylinder, we use a non-standard space-time discretization method, namely, the \emph{multiharmonic finite element and boundary element method}. This discretization technique yields large systems of linear algebraic equations, whereas the fast solution of these systems determines the efficiency of this method. Here, suitable preconditioners are needed in order to ensure \emph{efficient} and \emph{parameter-robust} convergence rates of the applied iterative method. Therefore, the main focus of this thesis lies on the construction and analysis of robust and efficient preconditioning strategies for the resulting systems of linear equations.