Uncertainty assessments are often considered as an ‘end of pipe’ analysis that is carried out on top of the modelling and expressed in purely statistical terms. This paper emphasises the importance of dealing with uncertainty throughout the modelling process and to consider also uncertainty aspects that can not be treated statistically. A discussion is provided on how uncertainty is addressed in different ways at different stages of the modelling process. An example of model structure uncertainty illustrates the importance of going beyond statistical uncertainty when assessing predictive uncertainty.