Gravitational waves are detected by measuring length changes between mirrors in the arms of kilometre-long Michelson interferometers. Brownian thermal noise arising from thermal vibrations of the mirrors can limit the sensitivity to distance changes between the mirrors, and, therefore, the ability to measure gravitational-wave signals. Thermal noise arising from the highly reflective mirror coatings will limit the sensitivity both of current detectors (when they reach design performance) and of planned future detectors. Therefore, the development of coatings with low thermal noise, which at the same time meet strict optical requirements, is of great importance. This article gives an overview of the current status of coatings and of the different approaches for coating improvement.This article is part of a discussion meeting issue 'The promises of gravitational-wave astronomy'.