  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, and the data analysis algorithms that have been
developed to address those challenges. I present a quantitative analysis of 297
continuous wave searches from 80 papers, published from 2003 to 2022, and
compare their sensitivities and coverage of the signal model parameter space.
