Gravitational lensing is a ubiquitous phenomenon in the Universe. We can leverage it to study cosmology - the properties of the Universe on its large scales - as well as the distribution of mass that caused the lensing, and the source of the light being lensed. Gravitational lensing is a precious tool, but some lenses are even more rare and useful than others: in this thesis, we are particularly interested in lensed quasars. Quasars are active galaxies powered by accretion onto their supermassive black holes, and are the brightest phenomenon in the Universe. They are in fact so bright that we can see them across the observable Universe. This makes them precious tools for cosmology, as their light is imprinted on by the expanding cosmological slab of space it crossed before reaching us. When the light of a quasar is additionally lensed by an intervening body of mass, such as a galaxy or a cluster of galaxies, it becomes an even more powerful cosmic laboratory. In particular, an important probe called Time Delay Cosmography (TDC) is enabled once the difference in arrival time between different lensed images of the same source is measured. Because quasars are intrinsically variable, monitoring a lensed quasar over time allows one to identify corresponding brightness variations in each image, thereby determining the time delay. Given a lens geometry and a cosmological model, TDC predicts the time delay value, which can then be compared to the measurement. This prediction of the delay is particularly sensitive to the Hubble constant, a cosmological parameter describing the present rate of expansion of the Universe. Any probe sensitive to this parameter is particularly relevant today, as the value predicted by the Concordance model of the Universe - LCDM - appears to be in tension with the measured one. However, while TDC is an important probe, like other techniques also sensitive to the Hubble constant, it suffers from potential systematic errors. The most important one stems from the Mass Sheet Degeneracy (MSD), a transformation of a lens model that leaves all observables invariant except the time delays. The bulk of this thesis covers my indirect contributions to TDC. In Chapter II, I present new lensed quasar systems and the novel techniques that permitted their finding. In Chapter III, the focus is shifted to one of these new lenses, PS J2107-1611, which has an alignment between the galaxy causing the lensing and the source quasar so good that it enables peering into the very engine of the quasar. Next, in Chapter IV, I present an overhauled infrastructure for the large-scale photometric deblending of compact objects, scaling to the next generation of telescopes and surveys. I also go over a multitude of new time delays that were measured from curves extracted with this new infrastructure. Chapter V is dedicated to the discovery and analysis of the first known instance of an Einstein zigzag - an exceedingly fortuitous alignment between two intervening galaxies and a quasar source - and I will argue that this system, J1721+8842, breaks the aforementioned MSD. Together with the extremely precise time delay we measured for this system, the hope is that it will provide stringent constraints on the Hubble constant. Finally, in Chapter VI, I present an excursion into inflationary phenomenology and its observables in the context of Higgs Palatini inflation.