Multiferroics are materials in which magnetism and ferroelectricity coexist. They are of fundamental interest to understand electronic behavior coupling magnetic interactions and electric dipolar order. Moreover, they are of applied interest because they allow various types of novel magnetic and electric device structures. We distinguish two important classes of multiferroic materials and discuss mechanisms and materials belonging to each class separately. In the first group of multiferroics, magnetization and polarization arise independently from each other. In the second category of multiferroics, ferroelectricity is induced by magnetic order, resulting in strong magnetoelectric coupling. We also briefly discuss multiferroic thin film heterostructures showing interfacial magnetoelectric coupling interactions with potential applications in memory devices