In this talk we show how modern theoretical and computational methods can be used to design technologically relevant electronic materials with dual- or multi-functionality. We choose multiferroic magnetoelectrics as an example; These are materials that are both ferromagnetic and ferroelectric in the same phase, and therefore have a spontaneous magnetization which can be switched by an applied magnetic field, a spontaneous polarization which can be switched by an applied electric field, and often some coupling between the two. Very few exist in nature, or have been synthesized in the laboratory, so we begin by determining the fundamental physics behind the scarcity of ferromagnetic ferroelectric coexistence. Then we identify the chemistry behind the additional electronic or structural driving forces that must be present for ferromagnetism and ferroelectricity to occur simultaneously. Finally we describe the successful prediction and subsequent synthesis of a new multiferroic material.