Using the Korteweg-de Vries-Burgers equation we will be presenting a brief but thorough introduction on the concept of dispersive shock waves. Dispersive shock waves are a phenomenon that occurs in nonlinear dispersive media, where traditional shock waves are modified by dispersive effects. Unlike classical shock waves that form sharp discontinuities when nonlinear steepening overcomes dissipation, dispersive shock waves develop into oscillatory structures. In dispersive media – where wave speed depends on wavelength or frequency – the dispersion relation prevents the formation of true discontinuities. Instead of a sharp shock front, these waves evolve into rapidly oscillating wave trains that connect two different uniform states, with oscillations that typically have decreasing amplitude away from the shock front and wavelengths much smaller than the overall system scale.