(Ga, Mn)As and other diluted magnetic semiconductors (DMS) attract a great deal of attention for potential spintronic applications because of the possibility of controlling the magnetic properties via electrical gating. Integration of a ferroelectric gate on the DMS channel adds to the system a non-volatile memory functionality and permits nanopatterning via the polarization domain engineering. This topical review is focused on the multiferroic system, where the ferromagnetism in the (Ga, Mn)As DMS channel is controlled by the non-volatile field effect of the spontaneous polarization. Use of ferroelectric polymer gates in such heterostructures offers a viable alternative to the traditional oxide ferroelectrics generally incompatible with DMS. Here we review the proof-of-concept experiments demonstrating the ferroelectric control of ferromagnetism, analyze the performance issues of the ferroelectric gates and discuss prospects for further development of the ferroelectric/DMS heterostructures toward the multiferroic field effect transistor.