Ecologists increasingly use complex models to predict and understand ecological systems and their responses to external drivers or anthropogenic pressures. An ongoing challenge in this context is quantifying and reducing uncertainty in model inputs, parameters and structure and understanding their implications for model predictions. Three major methodological fields have emerged in this context: sensitivity analysis, uncertainty analysis and model inversion or calibration. While these three methods are an integral part of any modelling or forecasting process, the corresponding literature is often scattered, and distinct terminology and definitions are used in different methodological and scientific contexts. Here, we review and connect these three fields and discuss best practices for their practical implementation with a focus on complex ecological models. We classify relevant types of uncertainty, discuss the complementary roles of sensitivity and uncertainty analyses, give an overview of available calibration methods and emphasize the importance of effective communication of uncertainty. We conclude that using state-of-the-art methods for understanding model behaviour as well as consistently accounting for all uncertainties is essential for correctly understanding model predictions and thus forms the basis for a responsible use of models in ecological decision making.