Electronic and vibrational transitions are characterized not only by energy and intensity, but also by direction. The measurement of transition moment directions in absorption is often experimentally simple and may provide essential information for assignment and recognition of transitions. It may also be used for determination of molecular alignment, structure, and conformation. Two-photon processes, such as luminescence, may provide even more detailed information of this kind. Applications of the techniques are found areas like materials science, microelectronics, and biochemistry and physics. The experimental determination of moment directions is frequently based on production of aligned samples, either by photoselection or by the use of anisotropic solvents, such as liquid crystals or stretched polymers. Two examples from absorption spectroscopy are used to illustrate the wide applicability of a simple, but frequently overlooked, experimental technique, as well as methods for interpretation of the spectra.