Fast radio bursts (FRBs) are millisecond-duration, highly-dispersed radio wavelength pulses. Based on their large dispersion measure, FRBs appear to originate from extragalactic distances implying extreme luminosities that are not seen in any galactic sources. Progress in understanding FRBs has been slow because the discovered events have had >arcminute localization, making association with galaxies or galactic objects impossible. Currently, there are more theories than FRBs, which number about 20. I will describe here the first arcsecond localization of an FRB. Using the Very Large Array (VLA) and other radio telescopes, we have shown that FRB 121102 is associated with a faint persistent radio source and a faint galaxy. Gemini observations provided the redshift (z~0.2) and identification of the galaxy as a dwarf with significant star formation and low metallicity. I will discuss the implications of this discovery for our understanding of FRBs and the possibility of using FRBs to study the intergalactic medium.