We propose convergent plasma lenses, possibly from current sheets, as a generic solution to strong interstellar scattering. These lenses resolve the overpressure problem by geometric alignment as noted by Goldreich & Shridhar. Our new model further quantitatively explains properties of extreme scattering events and pulsar parabolic arcs. It makes quantitative predictions testable by VLBI on scattering events. It differs conceptually from previous models by occurring through rare, localized underdense sheets. Such sheets are thermally and kinematically stable, and could be consequences of reconnection. The apparent diffractive effects are a result of coherent interference of refractive images. We propose that these lenses can be used for precision distance determination to pulsars, enabling accurate gravity source localization.