Since its early success as an experimental test of the theory of general relativity in 1919,gravitational lensing has come a long way and is firmly established as an indispensable elementfor many astrophysical applications. In this thesis, we explore novel applications of gravitationallensing that further our understanding of the dark sectors of the cosmos and other astrophysicalobjects, namely dark matter nanostructure, black holes and the Galactic disk. We pay particularattention to developing concrete and optimal statistical methodologies and numerical implemen-tations for these novel probes.We start by developing a statistical framework to measure the dark matter power spectrum inthe deep nonlinear regime, using transient weak lensing, and simultaneously measure the timedelays for strongly lensed quasars. We then outline how observations of microlensing in opticaland radio can unravel the structure, dynamics, and content of the Galactic disk, and in particular,be used to detect stellar mass black holes. Lastly, using the shadow images of the super-massiveblack holes caused by extreme lensing effect, we can learn about the structure of space-time,accretion flows and astrophysical jets. We present a Bayesian framework for analyzing the datafrom the Event Horizon Telescope Collaboration.
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Probing the dark universe with gravitational lensing