Muons can be used to explore a very diverse range of materials. Their applications broadly fall into two categories: using muons as probe particles to explore atomic level behaviour, and using muons as light protons to understand how hydrogen behaves in a material.

In the first case, muons can be used to explore a wide variety of magnetic and superconducting systems, and the muon can be thought of as acting like a very sensitive microscopic magnetometer. They can also be used to investigate molecular dynamics, together with charge transport phenomena such as polaron motion in conducting polymers, electron transport and ion conduction.

In the second case, the muon can be thought of as acting like a light proton. Muons can pick up an electron to form muonium, the analogue of a hydrogen atom. In materials where it is difficult to study proton or hydrogen atom behaviour directly, observing muon behaviour can provide a good guide to how hydrogen behaves. Following muon behaviour can also be useful to test models of light particle diffusion.