Multiferroic magnetoelectrics are materials which are both ferromagnetic and ferroelectric in the same phase. As a result they 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. In this paper we explore the fundamental physics behind the scarcity of ferromagnetic ferroelectric coexistence, and examine the properties of some known magnetically ordered ferroelectric materials. We find that in general the transition metaldelectrons, which are essential for magnetism, reduce the tendency for off-center ferroelectric distortion. Consequently, an additional electronic or structural driving force must be present for ferromagnetism and ferroelectricity to occur simultaneously. ©2000 American Institute of Physics.