The control of the group velocity of optical signals has been widely demonstrated using various optical phenomena and different media. Slow and fast light is achieved in a controllable manner by modifying the refractive index dispersion through light induced modifications of the material or the structural properties of the medium. The potential for a continuous tuning of the phase or time delay of broadband microwave signals modulating the optical carrier opens previously unexplored horizons. The talk will review the recent advancements and the future directions of slow and fast light research with an emphasis on microwave-photonics applications.