This review aims at providing a retrospective, as well as a description of the state-of-the-art and future prospects regarding the theoretical and experimental characterisation of negative-U defects in semiconductors. This is done by complementing the account with a description of the work that resulted in some of the most detailed, and yet more complex defect models in semiconductors. The essential physics underlying the negative-U behaviour is presented, including electronic correlation, electron-phonon coupling, disproportionation, defect transition levels and rates. Techniques for the analysis of the experimental data and modelling are also introduced, namely defect statistics, kinetics of carrier capture and emission, defect transformation, configuration coordinate diagrams and other tools. We finally include a showcase of several works that led to the identification of some of the most impacting negative-U defects in group-IV and compound semiconductors.