Radiation dose in x-ray computed tomography (CT) has become a topic of high interest due to the increasing numbers of CT examinations performed worldwide. This review aims to present an overview of current concepts for both scanner output metrics and for patient dosimetry and will comment on their strengths and weaknesses. Controversial issues such as the appropriateness of the CT dose index (CTDI) are discussed in detail. A review of approaches to patient dose assessment presently in practice, of the dose levels encountered and options for further dose optimization are also given and discussed. Patient dose assessment remains a topic for further improvement and for international consensus. All approaches presently in use are based on Monte Carlo (MC) simulations. Estimates for effective dose are established, but they are crude and not patient-specific; organ dose estimates are rarely available. Patient- and organ-specific dose estimates can be provided with adequate accuracy and independent of CTDI phantom measurements by fast MC simulations. Such information, in particular on 3D dose distributions, is important and helpful in optimization efforts. Dose optimization has been performed very successfully in recent years and even resulted in applications with effective dose values of below 1 mSv. In general, a trend towards lower dose values based on technical innovations has to be acknowledged. Effective dose values are down to clearly below 10 mSv on average, and there are a number of applications such as cardiac and pediatric CT which are performed routinely below 1 mSv on modern equipment.