Statistical iterative reconstruction is now widely used in clinical practice and has contributed to significant improvement in image quality in recent years. Although primarily used for reconstruction in emission tomography (both single photon emission computed tomography (SPECT) and positron emission tomography (PET)) there is increasing interest in also applying similar algorithms to x-ray computed tomography (CT). There is increasing complexity in the factors that are included in the reconstruction, a demonstration of the versatility of the approach. Research continues with exploration of methods for further improving reconstruction quality with effective correction for various sources of artefact.