Microlensing by stars within distant galaxies acting as strong gravitational lenses of multiply-imaged quasars, provides a unique and direct measurement of the internal structure of the lensed quasar on nano-arcsecond scales. The measurement relies on the temporal variation of high-magnification caustic crossings which vary on timescales of days to years. Multiwavelength observations provide information from distinct emission regions in the quasar. Through monitoring of these strong gravitational lenses, a full tomographic view can emerge with Astronomical-Unit scale resolution. Work to date has demonstrated the potential of this technique in about a dozen systems. In the 2020s there will be orders of magnitude more systems to work with. Monitoring of lens systems for caustic-crossing events to enable triggering of multi-platform, multi-wavelength observations in the 2020s will fulfill the potential of quasar microlensing as a unique and comprehensive probe of active black hole structure and dynamics.
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