•FAO56 advances in ET computation are retrospectively reviewed and analyzed.•Definition, procedures and advances in computing reference ET are reviewed.•Estimation, use and transferability of Kc's and their adjustment to local conditions are discussed.•The estimation of evaporation and transpiration with the dual Kc is analyzed.•ET estimation under non-standard conditions and with remote sensing are reviewed. The FAO Irrigation and Drainage Paper No 56 on Crop Evapotranspiration has been in publication for more than 15 years. The paper advanced the accuracy and consistency of operational computation of evapotranspiration (ET) for agricultural and other land use types. The paper included updated definition and procedures for computing reference ET, an update on estimating crop coefficients (Kc), the adoption of the dual Kc for separate estimation of crop transpiration and soil evaporation, and an upgraded estimation of crop ET under water and salt stress and other non-standard conditions. These advances are retrospectively reviewed in this paper. The advances in computing reference ET were primarily through the adoption of specific and consistent characteristics for the grass reference crop using the Penman–Monteith equation parameterized to represent a living reference surface. That standardization made the Kc more visual and understandable as a factor that relates the ET characteristics of a specific crop to the defined reference crop. Methodologies were introduced to estimate reference ET under conditions of limited weather data while retaining the use of the PM equation. Advances in adopted Kc research included techniques to estimate Kc based on the architecture of crops, notably height and fraction of ground cover. Other advances included consistent and straight-forward techniques for applying the dual Kc method via soil and evaporation process modeling on a daily timestep. New techniques were introduced for using yield response and salinity threshold values to estimate reductions in ET caused by elevated soil salinity. In addition, recommendations were given for adjusting ET for impacts of surface mulching, intercropping, and sparse vegetation. The successful adoption of the FAO–PM reference ET and Kc approaches owes primarily to the simplicity, yet relatively high level of robustness of the procedures, and to transferability and repeatability of the Kc method. Future development needs are discussed.