•Improvement of CT scanner hardware made a substantial contribution to the radiation dose reduction of computed tomography.•Current reduction, potential modification, and refinement of image production algorithms are the key dose reduction methods.•Automatic exposure control and iterative reconstruction methods play a significant role in the CT radiation dose reduction.•The validity of dose reduction can be evaluated with objective and subjective image quality, and diagnostic accuracy.•Realizing the reference dose level for common CT imaging protocols is necessary to avoid overdose in the CT examinations. Although radiation dose in computed tomography (CT) decreased and CT became safer examinations than before, CT is the most significant source of the medical radiation exposure. Knowledge about available radiation dose reduction methods in CT is essential. Substantial improvement occurred regarding tube current selection (automatic exposure control) and image production method (iterative reconstruction). Optimizing the tube potential selection is expected to contribute to further CT radiation dose reduction. This review article summarizes the principles of radiation dose reduction in CT, principal methods of radiation dose reduction, auxiliary measures of radiation dose saving and recent issues of low dose CT.