The isotropic-nematic (I-N) phase transition in hard ellipsoid fluids has been studied by computer simulation, using the Gibbs-Duhem integration technique introduced by Kofke; and theoretically, using Onsager theory and the Parsons-Lee improvement. In the simulations, the I-N coexistence line is mapped out in the P-x plane, where P is the pressure and x is the elongation, by numerically integrating a Clapeyron-like first-order differential equation, using constant-pressure simulation data for the two coexisting phases. The elongation range 5 less than or equal to x less than or equal to 20 has been studied, using independent starting points provided by chemical potential calculations and thermodynamic integration of the equation of state at x=5,20, plus a direct Gibbs ensemble simulation at x=20. The Onsager-Parsons-Lee theory has been applied to the I-N phase transition for aspect ratios up to x=1000, affording an accurate investigation of the approach to the Onsager limit for this model. This involved the numerical computation of the orientation-dependent second virial coefficient in a way that avoids expansions in Legendre polynomials, so as to be accurate at high elongation, Over the elongation range studied here, agreement between simulation and the Parsons-Lee theory is good.