The cosmological constant provides a simple explanation for the observed late-time accelerated expansion of our Universe. Our lack of understanding of it, however, motivates the exploration of alternative explanations such as a modification of General Relativity at cosmological scales. I will first discuss how gravitational wave observations have severely challenged that concept. I will then present a new self-tuning mechanism that provides a simple toy model to simultaneously solve both the old and new aspects of the cosmological constant problem. A possible signature of this mechanism is the variation of fundamental constants across different spacetime regions. I will briefly present new tools that can be used with forthcoming nonlinear cosmological data in the search for New Physics. Finally, I will explore the Emergence of Life across a potential multiverse as an approach to a deeper understanding of the fundamental parameters and laws of our own observable Universe.