Aquifers are intrinsically heterogeneous, but the interpretation of pumping tests to estimate hydraulic aquifer parameters, such as transmissivity and storativity, is commonly performed under the assumption of homogeneity, by utilizing Theis equation. This yields interpreted parameters whose relation to aquifer heterogeneity is uncertain. To optimize Theis-based pumping test interpretation techniques for the application to heterogeneous systems, this study investigates the relationship between the interpreted parameters and the underlying heterogeneity of aquifers. Two time-dependent spatial weighting functions are derived which enable the estimation of upscaled transmissivities from a given heterogeneous transmissivity distribution. The comparison of the upscaled transmissivities to the interpreted Theis-based transmissivities from synthetically generated pumping tests reveals that their meaning depends on the properties of the Theis solution, used during the interpretation process. If the interpreted transmissivity is estimated from the drawdown derivative it relates to an upscaled heterogeneous transmissivity field, but to an upscaled homogeneous transmissivity if the drawdown itself is used. This procedure is applied to infinite aquifers and to aquifers delimited by a linear constant head boundary (BCH). It is shown that Theis-based interpretation methods allow for assessing aquifer heterogeneity. Moreover, a new pumping test interpretation method for BCH aquifers is developed which allows for estimating the transmissivity continuously from the transient drawdown. The theoretical investigations are supplemented by the evaluation of real pumping tests in an aquifer system strongly affected by tectonics. In this regard, this study confirms that pumping test interpretation can provide fundamental information on reservoir boundaries and hydrogeological.