Computer simulations of the impact on climate of solar variability generally fall into four categories. First, there are lower atmosphere GCM experiments, in which enhanced solar activity is represented by changes in spectrally integrated solar constant. Secondly, there are GCM studies of the dynamical response of the middle atmosphere to changes in solar ultraviolet, mainly concentrating on the northern hemisphere winter, and how these impact the troposphere. These studies have been instructive in providing an understanding of some of the mechanisms involved but, because of the very different nature of the assumptions made, give rather different suggestions as to potential patterns of change. In particular predicted zonal mean temperature changes in the lower stratosphere are usually of opposite sign in these two types of experiment. None of these GCM studies include interactive photochemistry and the third category of modelling work is concerned with the photochemical response of the middle atmosphere to enhanced solar ultraviolet. These generally employ 2D models to predict changes in ozone and other gaseous species. Recently it has been realised that the responses (to a variety of external forcings) of the lower and middle atmospheres are linked through both radiative and dynamical mechanisms and should not be viewed in isolation from each other. Thus the fourth type of modelling study, which is still in its infancy, attempts to represent solar variability by realistic changes in both irradiance and ozone concentrations. In this paper these various modelling studies are reviewed and some new results presented which confirm previous theoretical suggestions that, in the northern hemisphere winter, the atmosphere may respond to solar changes in a similar way as to the injection of volcanic aerosol. The implications of the results of the model studies for the detection of solar-induced climate change are discussed.