A critical review of the various methods for determining regional effects indicates that neither the graphical systems nor the various numerical and mathematical systems provide a philosophically sound basis for separating a potential field into regional and residual components. The former depend on the judgment of the operator and the latter on assumptions or empirical steps in the mathematical derivation of the numerical factors or coefficients used in the calculations. Each system has its advantages and disadvantages and a proper appreciation of these is necessary for the successful application of either or both systems to a given problem.The various published mathematical systems are compared by reducing their numerical factors to a common basis and listing them in tabular form. This comparison shows the gross variation in numerical coefficients and weighting factors derived by different mathematical approaches. Comparisons of the graphical system and certain of the grid systems, made by carrying them out over a gravity map of the same area, show the effect of these variations on second derivative maps. Other examples of applications are listed from maps in the geophysical literature.It is concluded that the lack of an objective criterion for the isolation of anomalies is due to the inherent ambiguity in the sources of potential fields, but that in spite of the empirical nature of any regional method, the proper application of a system appropriate to the particular problem encountered can give very useful results.