Abstract We review the construction and use of complex potentials in reactive scattering and other molecular collisions to calculate continuum quantities (such as state-to-state transition probabilities, cumulative reaction probabilities, or resonance characteristics) with finite grid or finite basis methods. The success of the approach is greatly based on its simplicity. In general these potentials are adjusted phenomenologically or optimized for achieving an absorptive and non-reflecting boundary. For further progress the conceptual and formal framework of the complex potentials and the efficiency of their numerical implementation must be investigated more deeply. We present along this line a formal theory of scattering for complex potentials in one dimension, as well as a detailed account of the functional forms and construction methods proposed. We also demonstrate that part of the acquired knowledge may be transferred to “physical” absorbing potentials, i.e., effective interactions that can be tailored physically (rather than numerically) to accomplish e.g. an improved atomic detection by fluorescence.