Concrete creep models have to consider several important phenomena (non-linearity, multi-axiality, hydration, and thermal and drying effects) to be relevant in structural applications. A selection of experimental results of creep tests found in the scientific literature are used to highlight these phenomena. Firstly, regarding the creep rate in different directions of a specimen under various loads, it is shown that creep rate under moderate loading can derive from elastic strains. Secondly, the reason why a Drucker Prager criterion can be chosen to model non-linear creep is discussed. Thirdly the interest of resorting to a creep theory able to decouple ageing (or hydration) effects and consolidation effects is explained. Moreover, interest using a poro-mechanical formulation, in which Biot coefficient depends on stress state, to model drying creep and shrinkage is discussed in the light of short meso-scopic analysis. The effect of temperature on creep is also addressed. The numerical implementation of the proposed modelling is briefly exposed and the model responses are confronted with experimental results.