Methods for determination of absolute structure using X-ray crystallography are described, with an emphasis on applications for absolute configuration assignment of enantiopure light-atom organic compounds. The ability to distinguish between alternative absolute structures by X-ray crystallography is the result of a physical phenomenon called resonant scattering, which introduces small deviations from the inherent inversion symmetry of single-crystal X-ray diffraction patterns. The magnitude of the effect depends on the elements present in the crystal and the wavelength of the X-rays used to collect the diffraction data, but it is always very weak for crystals of compounds containing no element heavier than oxygen. The precision of absolute structure determination by conventional least squares refinement appears to be unduly pessimistic for light-atom materials. Recent developments based on Bijvoet differences, quotients and Bayesian statistics enable better and more realistic precision to be obtained. The new methods are sensitive to statistical outliers, and techniques for identifying these are summarised.