A muon is an unstable spin-½ particle with a lifetime of 2.2 ½s. Beams of spin-polarized positive muons can be prepared at accelerator facilities and then subsequently implanted in various types of condensed matter. Both the time and direction dependence of the subsequent positron emission can be monitored. This allows the precession and relaxation of the average muon-spin polarization to be measured and the local magnetic field in the sample to be directly inferred. The muon thus behaves essentially as a ‘microscopic magnetometer’ and is used to follow the magnetic order at a local level and to investigate both static and dynamic effects. This article outlines the principles of various experimental techniques that involve implanted muons, and reviews some recent experimental data on organic and molecular magnets.