X-ray Laue-type monochromators are common and essential optical components at many high-power X-ray facilities, e.g. synchrotron facilities. The X-ray optics of bent Laue crystals is a well developed area. An incident X-ray beam penetrating a bent Laue crystal will result in a diffracted beam with different angles and energies. There is a need for a way of organizing the rays that allows one to sort out the energy and spatial properties of the diffracted beam. The present work introduces a new approach for describing the general behaviour of bent Laue crystals from a ray-tracing point of view. This quasi-monochromatic beam approach provides an intuitive view of bent-crystal diffraction and leads to deeper understanding. It explains the energy and spatial properties of common and special cases of bent Laue optics, predicts phenomena that can improve energy-dispersion-related X-ray imaging techniques and provides a theoretical framework that makes ray-tracing simulation easier to realize.