The aim of sensitivity analysis is to apportion the uncertainty of the output of a simulation model with respect to its inputs. In spite of the considerable developments which have taken place in this discipline, of the good practices that have emerged, and of existing guidelines for sensitivity analysis issued on both sides of the Atlantic, very primitive sensitivity analysis tools, based on “one-factor-at-a-time” (OAT) approaches, are still being used (Campbell et al., 2008; Hasmadi and Taylor, 2008; Stites et al., 2007; Murphy et al. 2004;). In the context of model corroboration or falsification, this use of OAT methods is illicit and unjustified, unless the model under analysis is proved to be linear (Saltelli et al, 2008). In this talk we show that available good practices, such as variance based measures and screening methods, are able to overcome OAT shortcomings and are easy to implement. We illustrate new strategies for the efficient estimation of ‘total order' sensitivity indices, which are effective variance-based tools to quantify at what extent an individual model input can drive uncertainty in the model output by accounting for the presence of interactions between and other model inputs. A brief summary is given here to show the major features of variance-based methods. A Fourier implementation was developed in the seventies (Cukier et al. 1973), whereas antecedent works were made by Kolmogorov (see reviews Archer et al. 1997, Rabitz et al. 1999). However, the best systematization of the theory is due to Sobol' (Sobol 1990), while total sensitivity indices were introduced by Homma and Saltelli (1996). For reviews see also Saltelli et al. (2005), Helton et al. (2006) or Chapter 8 in Saltelli et al. (2000).