Three topics on modern shock capturing methods for the time-dependent Euler equations of Gas Dynamics are addressed. First we present the Weighted Average Flux Method (or WAF), one of several Riemann-problem based shock capturing methods. Then we deal with the Riemann problem. We present an efficient exact Riemann solver, a robust non-iterative Riemann solver based on the behaviour of the exact solver, and an improved version of the Harten-Lax-van Leer Riemann solver. Also, a very simple linearised Riemann solver is presented together with a Riemann solver adaptation procedure. We also present a Riemann-solver adaptation procedure that has proved successful. Applications of the WAF method with the various Riemann solvers are presented.Cranfield Institute of Technology