Magnetoresistance is the property of a material to change the value of its electrical resistance when an external magnetic field is applied to it. There is a variety of effects that can be called magnetoresistance, some of them occurring in bulk non-magnetic metals and semiconductors (e.g. geometrical magnetoresistance, Shubnikov de Haas oscillations or the common positive magnetoresistance in metals), others in magnetic metals (e.g. negative magnetoresistance in ferromagnets or AMR) and since 1980's magnetoresistive effects in multicomponent or multilayer systems (e.g. magnetic tunnel junctions) gained importance (GMR, TMR, EMR). The first magnetoresistive effect was discovered by William Thomson (better known as Lord Kelvin) in 1851, but he was unable to lower the electrical resistance of anything by more than 5%. Nowadays, systems are known (e.g. semimetals or concentric ring EMR structures) where magnetic field can change resistance by orders of magnitude. As the resistance may depend on magnetic field through various mechanisms, it is useful to separately consider situations where it depends on magnetic field directly (e.g. geometric magnetoresistance, multiband magnetoresistance) and those where it does so indirectly through magnetisation (e.g. AMR, TMR).