This paper examines the theoretical modeling of a steady horizontal gravity current involving miscible fluids. The main objective is to determine the longitudinal evolution of the current characteristic quantities: its mean velocity U, its height h, its mean density ρ, and the local Richardson number Ri = gρh/ρU2, which characterizes the flow regime. The theory developed by Ellison and Turner [J. Fluid Mech. 6, 423 (1959)] for Boussinesq gravity currents is first extended to the general non-Boussinesq case. In this theoretical approach, the differential equations derived from the conservation equations reveal a mathematical singularity which no longer allows them to be solved when the current passes from a supercritical to a subcritical regime, i.e., when the Richardson number reaches unity. To circumvent this problem, we propose to introduce a jump condition into the model which leads to a sudden transition from a supercritical to a subcritical regime when needed. The jump location is set to satisfy the boundary condition at the exit. Numerical simulations are carried out using a large-eddy simulation code in order to obtain reference results. These results are first used to select a suitable entrainment model among those proposed in the literature. The simulations are then compared with the theoretical model. In the case of a supercritical current without regime change, the agreement between simulation and theory is good. In the case of a supercritical current turning subcritical before the exit, the discontinuity imposed in the model by the jump is clearly abrupt in comparison with the physical reality, but it allows us to reproduce the nonmonotonic evolution of the velocity, height, and Richardson number of the current and to obtain an acceptable estimation of these quantities.