The present work presents a detailed study on the numerical calculation of impulsive and indicial unsteady aerodynamic responses with modern computational fluid dynamics solvers. A brief historical background on this subject is presented, and it is shown how new interpretations of computational fluid dynamics solvers as discrete-time systems change the way impulsive and indicial responses can be directly obtained. The objective is to demonstrate that the rigorous relationships theoretically established among the aerodynamic responses to impulse, indicial, harmonic, and smooth inputs can be numerically reproduced with modern computational fluid dynamics solvers. Although the numerical results presented herein are obtained with a single computational fluid dynamics tool, the argument is valid, in principle, for all numerical solution schemes. The computational fluid dynamics tool in question solves the two-dimensional Euler equations with an explicit time march, using a finite volume discretization which supports fully unstructured grids. The results are compared both in the time and in the frequency domains, which yields a more complete understanding of details of the numerical solutions.