Most particle accelerators today are expensive devices found only in the largest laboratories, industries, and hospitals. Using techniques developed nearly a century ago, the limiting performance of these accelerators is often traceable to material limitations, power source capabilities, and the cost tolerance of the application. Advanced accelerator concepts a aim to increase the gradient of accelerators by orders of magnitude, using new power sources (e.g. lasers and relativistic beams) and new materials (e.g. dielectrics, metamaterials, and plasmas). Worldwide, research in this area has grown steadily in intensity since the 1980s, resulting in demonstrations of accelerating gradients that are orders of magnitude higher than for conventional techniques. While research is still in the early stages, these techniques have begun to demonstrate the potential to radically change accelerators, making them much more compact, and extending the reach of these tools of science into the angstrom and attosecond realms. Maturation of these techniques into robust, engineered devices will require sustained interdisciplinary, collaborative R&D and coherent use of test infrastructure worldwide. The outcome can potentially transform how accelerators are used.