In this paper a survey is given of the theoretical contributions essential for the derivation of regional investment functions of material infrastructure. A basic distinction is made between models of investment volume (level models) and investment-programming models (structure models). Investment functions may also be obtained from structure models by parametric programming that may be subsumed under those types of functions stemming from level models. In addition, empirical research on investment functions in selected fields of regional water-quality management, electricity supply, and provision of telephone services is summarized with respect to the main theoretical approaches—the accelerator models and the neoclassical cost model. To a substantial extent this research uses unpublished data for regression analysis.