Physics Colloquium 29th May 2015 delivered by Professor Cary Forest Most astrophysical plasmas are often characterized by turbulent, flowing plasma in which the flow energy is continuously transformed into magnetic energy through the dynamo process. Understanding this energy transformation and predicting what form the magnetic field might take, be it small-scale turbulent magnetic fields or large scale magnetic flux is the dynamo problem. In this review, I will give an overview of the taxonomy of magnetic fields observed in nature, including those of stars, disks, galaxies and clusters of galaxies. Dynamos can be classified as small-scale or large-scale. Small-scale dynamos tend to generate magnetic energy but little net magnetic flux, whereas large-scale dynamos generate both net flux and energy. While the mechanism by which magnetic energy at small-scales is generated is now well understood, how a large scale field self-organizes from small-scale magnetic fluctuations clusters is a grand challenge for plasma astrophysics. Theoretical dynamos studies are now focused on understanding how subcritical transitions make some dynamos essentially non-linear and also how dynamos in nearly collisionless plasmas may differ from MHD dynamos. I will finish by reviewing how dynamo experiments have and may inform us about astrophysical dynamos.