This paper reviews the research on the FAO56 single and basal crop coefficients of fruit trees and vines performed over the past twenty-five years and focus on Mediterranean and warm temperate trees and vines. Two companion papers (López-Urrea et al., (2023) Single and basal crop coefficients for estimation of water use of tree and vine woody crops with consideration of fraction of ground cover, height, and training system for temperate climate fruit crops. Irrig Sci (submitted); Paredes et al. (2023) Single and basal crop coefficients for estimation of water use of tree and vine woody crops with consideration of fraction of ground cover, height, and training system for tropical and subtropical fruit crops. Irrig Sci (submitted)) are dedicated, respectively, to Temperate and to Tropical and Subtropical trees and vines. The main objective of the paper is to update available information on single (Kc) and basal (Kcb) standard crop coefficients, and to provide for updating and completing the FAO56 tabulated Kc and Kcb. The Kc is the ratio between non-stressed crop evapotranspiration (ETc) and the grass reference evapotranspiration (ETo), while Kcb is the ratio between crop transpiration (Tc) and ETo. The selection and analysis of the literature were performed considering only studies that adhere to the FAO56 method, thus computing ETo with the FAO Penman–Monteith ETo equation, the ASCE grass ETo, or another equation that could be properly related with the former, and ETc, or Tc, was obtained using properly accurate field measurements on crops under pristine or eustress conditions. The crops considered refer to Mediterranean (grapes and olive) and warm temperate areas (avocado, citrus, persimmon, loquat, and tea) fruit and leaf crops. Papers satisfying the above conditions were selected to provide for standard Kc and Kcb data. Preferably, studies should report on the crop cultivar and rootstock, planting density or plant spacing, fraction of ground cover (fc), crop height (h), crop age and training systems. Additional information was collected on pruning and irrigation method and strategy. The ranges of reported Kc and Kcb values were grouped according to crop density in relation with fc, h, and the training system, namely vase, hedgerow, or trellis systems. Literature collected Kc or Kcb values were compared with previously tabulated Kc and Kcb values, namely in FAO56, to define the standard Kc and Kcb values for the referred selected crops. The tabulated values are, therefore, transferable to other locations and aimed for use in crop water requirement computations and modeling, mainly for irrigation planning and scheduling, and for supporting improved water use and saving in orchards and vineyards.