Atomic force microscopy is a versatile technique allowing to exploit many different physical effects for measuring a number of materials properties. The magnetic properties of surfaces and thin films are traditionally accessed through magnetic force microscopy, which produces magnetic field gradient maps generated by the magnetisation distribution at the surface of the sample. However, more advanced techniques can be derived from this fundamental setup, allowing for a richer characterisation of magnetic samples. In this chapter, we will describe how to extend a magnetic force microscope to allow magnetic field-dependent characterisations. Magnetisation reversal processes, as well as full hysteresis loops, can be investigated with such a technique, with field resolution adequate for identifying significant features such as domains reversal, nucleation or annihilation of domains, and other irreversible mechanisms. The same principle can also be exploited for the measurement of magnetostriction on thin films, and can be taken as guideline for other advanced applications of atomic force microscopy.