This review describes a particular class of neutral defect complexes in GaP, represented by the variety of Cu-related centres, which are observed to bind excitons in a spin-like singlet-triplet configuration. The reasons for this are discussed and two subgroups are defined. One of these consists of centres which bind holes in localized orbitally nondegenerate spin states, but give rise to highly structured optical spectra. The other group is characterized by featureless photoluminescence spectra in the mid-gap spectral region due to a tight binding of both the electron and hole in spin-like states. Both groups are well described with an essentially identical spin-Hamiltonian formalism, as detailed optically detected magnetic resonance measurements have revealed. The relation of this class of neutral defects in GaP to similar complexes in other semiconductors is discussed.