Most ferromagnetic and antiferromagnetic substances show a simple collinear arrangement of the local spins. Under certain circumstances, however, the spin configuration is non-collinear. Scanning tunneling microscopy with its potential atomic resolution is an ideal tool for investigating these complex spin structures. Non-collinearity can be due to topological frustration of the exchange interaction, due to relativistic spin-orbit coupling or can be found in excited states. Examples for all three cases are given, illustrating the capabilities of spin-polarized scanning tunneling microscopy.