We review current knowledge of the processes by which ozone will cause injury and damage to crop plants. We do this both through an understanding of the limitations to ozone uptake (i.e. ozone being transferred from some height in the atmosphere to the leaf boundary layer and subsequent uptake via the stomata) as well as through the internal plant processes that will result in the absorbed ozone dose causing damage and/or injury. We consider these processes across a range of scales by which ozone impacts plants, from cellular metabolism influencing leaf level physiology up to whole canopy and root system processes and feedbacks. We explore how these impacts affect leaf level photosynthesis and senescence (and associated carbon assimilation) as well as whole canopy resource acquisition (e.g. water and nutrients) and ultimately crop growth and yield. We consider these processes from the viewpoint of developing crop growth models capable of incorporating key ozone impact processes within modelling structures that assess crop growth under a variety of different abiotic stresses. These models would provide a dynamic assessment of the impact of ozone within the context of other key variables considered important in determining crop growth and yield. We consider the ability to achieve such modelling through an assessment of the different types of crop model currently available (e.g. empirical, radiation use efficiency, and photosynthesis based crop growth models). Finally, we show how international activities such as the AgMIP (Agricultural Modelling and Improvement Intercomparison Project) could see crop growth modellers collaborate to assess the capabilities of different crop models to simulate the effects of ozone and other stresses. The development of robust crop growth models capable of including ozone effects would substantially improve future national, regional and global risk assessments that aim to assess the role that ozone might play under future climatic conditions in limiting food supply.