The use of Computational Fluid Dynamics (CFD) for predicting aerodynamic flows has burgeoned in the past two decades. The use of such aerodynamic computations for predicting drag for aircraft configurations still poses considerable difficulties. After reviewing some concepts in the numerical analysis of the equations of fluid flow, the fundamental difficulties in the prediction of drag using CFD are considered. Successes and failures in computing drag are examined to shed light on where improvements in the numerical analysis of fluid flow are required. An examination of the emerging CFD technologies is presented to assess how improvements in the computational techniques may result in improved drag predictions.