•Hot deformation behavior and constitutive description of flow stress for HEAs are summarized.•Effects of deformation conditions, phases, and dynamic precipitation are discussed.•Necklace DRX and the effects of processing parameters on the DRX grain size are discussed.•Constitutive modeling techniques for the prediction of flow stress of HEAs are critically discussed.•Future prospects in the field of hot deformation and constitutive modeling of HEAs are listed. Display omitted This review article summarizes the hot deformation behavior of high entropy alloys (HEAs) and the corresponding constitutive description of flow stress. The potential of hot working for grain refinement via dynamic recrystallization (DRX), reduction of casting defects, and enhancement of mechanical properties of HEAs is explained. The necklace formation, work hardening analysis for identification of the occurrence and initiation of DRX, and the effects of processing parameters on dynamically recrystallized grain size are discussed. The effects of deformation conditions (represented by the Zener-Hollomon parameter), alloying elements, dynamic precipitation, and the presence of phases on the hot deformation behavior and restoration processes of DRX and dynamic recovery (DRV) are overviewed. The application of processing maps for the characterization of the onset of flow instability, cracking, flow softening, and DRX during hot forming of HEAs is presented. Regarding the constitutive modeling of flow stress for characterization of material flow (at different deformation temperatures, strain rates, and strain), the utilization of the threshold stress (due to the presence of phases or their precipitation during high-temperature deformation), and temperature-dependent Young’s modulus, as well as correlating the obtained values of deformation activation energy and stress exponent with the expected ones from the creep theories are taken into account. Afterward, the available methods and equations for modeling and prediction of flow curves during thermomechanical processing are assessed, where the strain-compensated Arrhenius model, artificial neural network (ANN) model, Zerilli-Armstrong model, Johnson-Cook model, Hensel-Spittel model, and dislocation density-based multiscale constitutive model are presented. Finally, some suggestions for future research works are proposed.