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Evaluation of image quality (IQ) in Computed Tomography (CT) is important to ensure that diagnostic questions are correctly answered, whilst keeping radiation dose to the patient as low as is reasonably possible. The assessment of individual aspects of IQ is already a key component of routine quality control of medical x-ray devices. These values together with standard dose indicators can be used to give rise to 'figures of merit' (FOM) to characterise the dose efficiency of the CT scanners operating in certain modes. The demand for clinically relevant IQ characterisation has naturally increased with the development of CT technology (detectors efficiency, image reconstruction and processing), resulting in the adaptation and evolution of assessment methods. The purpose of this review is to present the spectrum of various methods that have been used to characterise image quality in CT: from objective measurements of physical parameters to clinically task-based approaches (i.e. model observer (MO) approach) including pure human observer approach. When combined together with a dose indicator, a generalised dose efficiency index can be explored in a framework of system and patient dose optimisation. We will focus on the IQ methodologies that are required for dealing with standard reconstruction, but also for iterative reconstruction algorithms. With this concept the previously used FOM will be presented with a proposal to update them in order to make them relevant and up to date with technological progress. The MO that objectively assesses IQ for clinically relevant tasks represents the most promising method in terms of radiologist sensitivity performance and therefore of most relevance in the clinical environment.