'Quantum mixtures dominate the physics of helium liquids, neutron stars, nuclear matter, quark-gluon plasma, quantum magnets and superconductors, but these systems are so dense that their complete understanding remains a distant goal. Ultracold quantum mixtures of two bosonic gases constitute an ideally-tunable platform which allows for a complete control over interactions, temperature, and dimensionality, an in-depth understanding of the physics at stake, and the exploration of radically new phenomena. In state-of-the-art experiments on these mixtures, small clusters of atoms (1000-10000) were shown to become self-bound and highly-incompressible, due to the balance of attractive and repulsive forces. First observed in 2017, these liquid droplets constitute a new state of matter, much denser than quantum gases, but orders of magnitude more dilute and colder than any other liquid in Nature. A key property of these systems is that mean-field interactions are tuned to be overall weakly-attractive, so that the stabilization mechanism which leads to droplet formation is provided only by quantum fluctuations. In mixtures where atoms of one component largely outnumber the others, the minority atoms become dressed by majority collective excitations forming Bose polarons, first observed in 2016. When polarons are immersed in a weakly-interacting bath, a controlled theoretical approach is possible even when polaron-bath interactions are strong. Droplets and polarons constitute, respectively, the balanced and the highly-imbalanced limits of quantum mixtures, and the 'UltraLiquid' project will lay theoretical firm ground for the unified description of their dynamics and thermodynamics, which will direct future experiments, and in close collaboration with our team. These systems allow for far-reaching investigations of quantum many-body effects and high-resolution measurements inconceivable so far. These promise innovative applications in quantum metrology and quantum sensing.'