The identification of causal effects and influential variables related to some phenomena of interest is one of the fundamental issues in many socio-environmental studies. In the context of regression analysis, importance measures are effective tools to perform feature selection or to interpret a model by ranking the most influential regressors. In particular, variance-based importance measures (VIMs) are prominent in the field of statistics, but also in the most recent field of global sensitivity analysis, due to their accessible interpretation as variance shares of the explained variable. By focusing on the linear regression model, this work aims at revisiting the overview of the most well-founded methods (some of them being rather old and sometimes, misunderstood), while clarifying their respective positioning, conditions of use, intrinsic capabilities, and interpretation. Some challenges are discussed, such as the case of dependent inputs and the case of a high input dimension. The practical relevancy of such tools is highlighted through their empirical study on simulated data, as well as public datasets. Other test cases, as well the use of the VIMS in a classification context (via the logistic linear regression model), are also presented in the supplementary materials.