Strong lensing time-delay cosmography in the 2020s

Abstract: Multiply imaged time-variable sources can be used to measure absolute distances as a function of redshifts and thus determine cosmological parameters, chiefly the Hubble Constant H$_0$. In the two decades up to 2020, through a number of observational and conceptual breakthroughs, this so-called time-delay cosmography has reached a precision sufficient to be an important independent voice in the current ``Hubble tension'' debate between early- and late-universe determinations of H$_0$. The 2020s promise to deliver major advances in time-delay cosmography, owing to the large number of lenses to be discovered by new and upcoming surveys and the vastly improved capabilities for follow-up and analysis. In this review -- after a brief summary of the foundations of the method and recent advances -- we outline the opportunities for the decade and the challenges that will need to be overcome in order to meet the goal of the determination of H$_0$ from time-delay cosmography with 1\% precision and accuracy.