We review our recent work on ferromagnet/semiconductor hybrid structures. In particular we focus on magnetotransport experiments performed on Co/InAs/Co hybrid structures fabricated on the cleaved edge of an InAs/InGaAs heterostructure. By modulation doping we inserted a high-mobility two-dimensional electron system (2DES) between the Co source and drain contacts which were separated by about 0.2 µm. This separation was smaller than the mean free path in the 2DES. Two additional metallic gate electrodes were integrated, thus forming a prototype spin field-effect transistor on a cleaved (110) surface of an InAs/InGaAs heterostructure. Intriguingly, we observe two characteristic magnetotransport signals at 4.2 K: (a) a hysteretic spin-valve-like signal and (b) a large positive magnetoresistance. We attribute the latter to the extraordinary magnetoresistance effect, i.e. the magnetic-field induced current redistribution between the Co contacts and the 2DES.