Positrons are antiparticles of electrons that can serve as ultrasensitive probes of atomic-level structural detail in materials. When positrons annihilate with electrons, characteristic γ-rays are produced. Positron annihilation spectroscopy is based on the detection of the γ-photons emitted in the positron–electron annihilation process, and experimental methods analyse the time, energy and angular distributions of these γ-photons. In crystalline solids, the selective sensitivity of positrons to vacancy defects allows one to identify their structure and to determine their concentrations and physical properties in a wide range of materials. This Primer presents techniques in positron annihilation spectroscopy, evaluates the typical results obtained and highlights recent advances across various fields, ranging from point defects and porosity in solids to material surfaces and interfaces. This Primer provides an introduction to positron annihilation spectroscopy and its uses in studying atomic-scale structures in solids.