An introduction to spin-polarized scanning tunneling microscopy with a soft magnetic tip is given. After illustrating the fundamental physical effort of tunneling magnetoresistance and giving a short historical background, it is shown how magnetic and topographic information can be separated using a modulation technique of the tip magnetization. Important for the functionality of the method is to avoid magnetostriction in the tip during reversal of its magnetization. It is shown tht this is theoretically and experimentally possible with an appropriate tip material of very low magnetostriction. The closure domain structure of Co(0001) is studied and ultrasharp 20 ^° domain walls of only 1.1 nm width are found. This narrow width is explained on the basis of a micromagnetic model, and a lateral resolution of the technique better than 1 nm is shown. The limits of the technique due to the stray field of the magnetic tip are illustrated. In the case that the stray field of the tip influences the sample under investigation, the local magnetic susceptibility can be measured. Furthermore, we focus on the contrast mechanism and give evidence that the tunneling magnetoresistance depends on the barrier height in agreement with Slonczewski's model. Finally, the possibility of magnetic imaging through a non-magnetic overlayer is discussed.