To explain the technical principles of and differences between commercially available iterative reconstruction (IR) algorithms for computed tomography (CT) in non-mathematical terms for radiologists and clinicians. Technical details of the different proprietary IR techniques were distilled from available scientific articles and manufacturers' white papers and were verified by the manufacturers. Clinical results were obtained from a literature search spanning January 2006 to January 2012, including only original research papers concerning IR for CT. IR for CT iteratively reduces noise and artefacts in either image space or raw data, or both. Reported dose reductions ranged from 23 % to 76 % compared to locally used default filtered back-projection (FBP) settings, with similar noise, artefacts, subjective, and objective image quality. IR has the potential to allow reducing the radiation dose while preserving image quality. Disadvantages of IR include blotchy image appearance and longer computational time. Future studies need to address differences between IR algorithms for clinical low-dose CT. • Iterative reconstruction technology for CT is presented in non-mathematical terms. • IR reduces noise and artefacts compared to filtered back-projection. • IR can improve image quality in routine-dose CT and lower the radiation dose. • IR's disadvantages include longer computation and blotchy appearance of some images.