The adiabatic quantum-flux-parametron (AQFP) is an energy-efficient superconductor logic element based on the quantum flux parametron. AQFP circuits can operate with energy dissipation near the thermodynamic and quantum limits by maximizing the energy efficiency of adiabatic switching. We have established the design methodology for AQFP logic and developed various energy-efficient systems using AQFP logic, such as a low-power microprocessor, reversible computer, single-photon image sensor, and stochastic electronics. We have thus demonstrated the feasibility of the wide application of AQFP logic in future information and communications technology. In this paper, we present a tutorial review on AQFP logic to provide insights into AQFP circuit technology as an introduction to this research field. We describe the historical background, operating principle, design methodology, and recent progress of AQFP logic.