A theoretical approach to Optical Nuclear Polarisation (ONP) is described, which is based on the analysis of Level Anti-Crossings (LACs) in triplet states. Here we consider ONP formed in molecular crystals doped with suitable guest molecules and ONP generated in diamond crystals containing negatively charged nitrogen-vacancy (NV–) centres. In both cases, electron spin polarisation of triplet states generated by light excitation is transferred to nuclei giving rise to ONP. Polarisation transfer is most efficient at LACs; for this reason, we consider in detail crossings of electron–nuclear energy levels and the role of different perturbation terms (coming from isotropic and anisotropic hyperfine coupling, zero-field splitting and sample orientation), which turn these crossings into LACs and give rise to ONP. Analytical results are supported by numerical calculations of the ONP field dependences. Thus, the outlined LAC analysis is a useful approach for interpreting the ONP magnetic field dependence.