This paper intends to give a state of the art overview on the experimental and theoretical studies regarding masonry creep, considering several papers published on this subject in the last two decades. Both new and historic masonry are addressed. Linear viscoelastic behaviour can be assumed in the analysis of masonry under service loads, whereas damage effects must be taken into account when analyzing the effects of heavy sustained loads, as in the case of several historic buildings. Finally, some applications are shown of a model to the prediction of the time evolution of creep-induced damage in historic masonry towers