For the monodomain approximation of the bidomain equations, a weak solution concept is proposed. We analyze it for the FitzHughNagumo and the RogersMcCulloch ionic models, obtaining existence and uniqueness theorems. Subsequently, we investigate optimal control problems subject to the monodomain equations. After proving the existence of global minimizers, the system of the first-order necessary optimality conditions is rigorously characterized. For the adjoint system, we prove an existence and regularity theorem as well.