Time-delay strong lensing (TDSL) provides a distance probe that is independent of both the local distance ladder and the cosmic microwave background calibration. Its primary observable is the relative arrival time of multiple images, while the conversion of this delay into DΔt and H0 requires a joint inference of the lens potential and the variable source. This review summarizes the current status of TDSL measurements from lensed quasars and lensed supernovae in the context of the Hubble tension. We then review the basic lensing equations and the modeling ingredients that dominate present analyses, including mass-profile assumptions, line-of-sight corrections, stellar kinematics, microlensing, and source structure. The discussion follows how these terms enter the Fermat-potential reconstruction, the measured time delay likelihood, and the final uncertainty on DΔt and H0. We also discuss quasar accretion-disk microlensing as a related application, since the same finite and wavelength-dependent source structure that perturbs QSO light curves can also be used to constrain the accretion-disk size and temperature profile. Finally, we describe the role of the Muztagh-Ata 1.93 m Synergy Telescope in future monitoring of lensed quasars and lensed supernovae.