Spin-polarized scanning tunnelling microscopy is applied to study the growth of Fe on Cr(001) as well as the dependence of the electronic and magnetic structure on the Fe coverage. Topographic measurements show an almost perfect layer-by-layer growth except for the coverage range 1.48 ML < theta < 3 ML, where the second and third layers grow simultaneously. By high-temperature annealing, alloying between the Cr substrate and the Fe film is provoked. Scanning tunnelling spectroscopy (STS) shows that the electronic structure of the resulting c(2 x 2)-ordered Fe/Cr alloy is governed by a double peaked dI/dU spectrum with maxima at U = -0.3 and +0.15 V. A time-dependent STS investigation of Fe/Cr(001) reveals that the interface is structurally unstable against alloying. While the spectra are dominated by a single d(z)2-like surface state on the day of preparation a double-peak spectrum, indicating the presence of a Fe/Cr alloy, was found one day after preparation. Spin-resolved measurements show that, at small coverage (theta less than or equal to 0.2 ML), the Fe islands couple antiferromagnetically to the underlying Cr(001) terraces. The magnetic contrast of the islands and the substrate starts to decrease for theta greater than or equal to 0.22 ML and completely vanishes at theta greater than or equal to 0.4 ML. This observation is discussed in terms of a reduction of the Cr Neel temperature due to interdiffusion of Fe into the interface-near region of the Cr substrate. For theta greater than or equal to 3 ML a weak magnetic contrast reappears which is possibly caused by a spatial variation of the 90degrees coupling between the Cr substrate and the Fe overlayer.