As a result of the increase in penetration of inverter-based generation such as wind and solar, the dynamics of the grid are being modified. These modifications may threaten the stability of the power system since the dynamics of these devices are completely different from those of rotating generators. Protection schemes need to evolve with the changes in the grid to successfully deliver their objectives of maintaining safe and reliable grid operations. This paper explores the theory of traveling waves and how they can be used to enable fast protection mechanisms. It surveys a list of signal processing methods to extract information on power system signals following a disturbance. The paper also presents a literature review of traveling wave-based protection methods at the transmission and distribution levels of the grid and for AC and DC configurations. The paper then discusses simulations tools to help design and implement protection schemes. A discussion of the anticipated evolution of protection mechanisms with the challenges facing the grid is also presented.