In less than a decade, fast radio bursts have gone from a single debated curiosity to a diverse extragalactic population with established host galaxies and energy scales. While a wide range of models remain viable, the central engines of FRBs are likely to involve energetic young magnetars, as confirmed by the recent discovery of a Galactic analog to these extragalactic bursts. Here we provide a brief introductory review of fast radio bursts, focusing on the rapid recent progress in observations of these enigmatic events, our understanding of their central engines, and their use as probes of the intergalactic medium. We caution against a rush to judgement on the mechanisms and classification of all FRBs: at this point, it remains plausible that there could be one dominant central engine, as well as the possibility that radio bursts are a generic feature produced by many different mechanisms. We also emphasize the importance of improved modeling of our Galaxy and Galactic halo, which otherwise impose systematic errors on every FRB line of sight. The future of science with fast radio bursts appears bright.