Methods for quasar absorption system measurements of the fine structure constant in the 2020s and beyond

This article reviews the two major recent developments that significantly improved cosmological measurements of fundamental constants derived from high resolution quasar spectroscopy. The first one is the deployment of astronomical Laser Frequency Combs on high resolution spectrographs and the second one is the development of spectral analysis tools based on Artificial Intelligence methods. The former all but eliminated the previously dominant source of instrumental uncertainty whereas the latter established optimal methods for measuring the fine structure constant ($\alpha$) in quasar absorption systems. The methods can be used on data collected by the new ESPRESSO spectrograph and the future ANDES spectrograph on the Extremely Large Telescope to produce unbiased $\Delta\alpha/\alpha$ measurements with unprecedented precision.