HAWC observations have detected extended TeV emission coincident with the Geminga and Monogem pulsars. In this talk, I will show that these detections have significant implications for our understanding of pulsar emission. First, the spectrum and intensity of these “TeV Halos” indicates that a large fraction of the pulsar spindown energy is efficiently converted into electron-positron pairs. This provides observational evidence necessitating pulsar interpretations of the rising positron fraction observed by PAMELA and AMS-02. Second, the isotropic nature of this emission provides a new avenue for detecting nearby pulsars with radio beams that are not oriented towards Earth. Third, these observations indicate that the total emission from unresolved pulsars produces the majority of the TeV gamma-ray flux observed from the Milky Way.