A large number of numerical algorithms have been reported to solve the Euler equations of motion for a variety of Mechanical and Aerospace Engineering applications. Based on a review of the past and current history of these solvers, a MUSCL-based solver that uses Hancock's Predictor-Corrector Method incorporating Roe's Approximate Riemann Solver was found to be the most efficient second-order accurate numerical method to solve the Euler equations. This method was subsequently extended to account for variable properties and then extensively validated for the effects of friction, heat transfer, variable area and chemical kinetics.