The growing demand for higher computing power and element density continuously drives the development of novel device concepts. One group of materials currently attracting a lot of interest are the magnetoelectric multiferroics, due to their potential for creating devices with novel functionalities. These materials exhibit coupled ferroelectric and ferromagnetic behavior. Although the focus is on homogeneous multiferroics like bismuth ferrite, the stronger multiferroic coupling that is possible in composite multiferroics makes them attractive for many potential applications (e.g. spintronic logic and memory elements). In particular, electric field-mediated multiferroic composites promise worthwhile compatibility with CMOS circuitry. The present work explores a multiphase multiferroic system where the ferroelectric gate controls a dilute magnetic semiconductor (DMS) channel via the nonvolatile field effect associated with the spontaneous polarization. The system consists of a copolymer of vinylidene fluoride and trifluoroethylene [P(VDF-TrFE)] as the ferroelectric gate and an ultra-thin magnetic layer of (Ga,Mn)As which is one of the most well-established DMS and is considered a chief candidate for spintronic applications. The main outcomes of this research can be summarized as follows: A widely recognized incompatibility between ferroelectrics and group III-V semiconductors has been solved by the integration of a polymer ferroelectric onto a DMS in a multiferroic transistor configuration. Nonvolatile electric field control of ferromagnetism in a (Ga,Mn)As channel has been successfully demonstrated. Several pieces of evidence including the change of hysteretic properties, ferromagnetic Curie temperature shift and magnetoresistance behavior attest to the field effect-mediated multiferroic coupling in this system. Low ferroelectric gate operation voltages below 10 V were achieved through aggressive P(VDF-TrFE) thickness reduction without diminishing the gate effect strength. Polarization screening at the semiconductor/ferroelectric interface was identified as the main issue limiting the ferroelectric gate effect. A significant enhancement of the multiferroic coupling has been reached by thinning the (Ga,Mn)As channel down to 3 nm without compromising the ferromagnetic properties. From the Curie temperature response to ferroelectric gating, that follows the same trend for samples with thicknesses ranging from 3 to 7 nm, we conclude that the 2D limit has not been reached for the thinnest channels and the 3D models describing the ferromagnetic coupling are valid for this case. The ferroelectric control of ferromagnetism has been quantitatively interpreted in terms of existing models for hole-mediated exchange in (Ga,Mn)As.