Seven years after the first direct detection of gravitational waves, from the collision of two
black holes, the field of gravitational wave astronomy is firmly established. A first detection of
continuous gravitational waves from rapidly-spinning neutron stars could be the field's next
big discovery. I review the last twenty years of efforts to detect continuous gravitational
waves using the LIGO and Virgo gravitational wave detectors. I summarise the model of a
continuous gravitational wave signal, the challenges to finding such signals in noisy data …