In the era of precision cosmology, a wide range of cosmological surveys, such as LSST of Rubin Observatory, DESI, Euclid and Roman Space Telescope will precisely probe the large-scale structure and expansion history of the universe, shedding light on the nature of the dark sector. The unprecedented high-quality data from upcoming weak lensing surveys is expected to reduce the statistical uncertainty in weak lensing measurements compared
to current surveys by roughly an order of magnitude. This will be an opportunity to explore mysteries in contemporary cosmology, including the apparent tensions between the
early and the late universe as well as the nature of dark energy and dark matter. In the next generation of weak lensing surveys, the analysis requires a better understanding and more careful control of systematic uncertainties to avoid their dominating over statistical
uncertainties. Low-level sources of systematic uncertainty that are presently ignored in current weak lensing analyses will become significant as the precision of the measurements increases.