This review deals with thin films of single-phase materials which exhibit two primary ferroic properties, namely ferroelectricity and (anti)ferromagnetism, deposited directly or through buffer layers onto semiconductors. It is the electrical control of ferromagnetism and magnetic control of ferroelectricity at room temperature and resulting device functionality that served as the driving force for the recent widespread research activities in this field. Although Gilbert demonstrated in 1600 that electrostatics (amber) do not couple to magnetostatics (compass needles), charges in motion certainly couple to magnetism, as shown later by Oersted and epitomized by Maxwell's theoretical derivation of the properties of electromagnetic waves. We survey the important contributions of various eminent physicists, from Curie to Dzyaloshinskii and Astrov to Schmid, without whom this field of research might not have developed. Most of the known multiferroic materials are classified into different groups, primarily based on Khomskii's classification of oxide multiferroics. We follow this with a brief discussion on the device application of multiferroics with semiconductor integration.