I will discuss how the past few years have witnessed a major change in our understanding of cluster formation and destruction. The classical picture of infant mortality (all stars form in clusters of which 90-95% subsequently dissolve due to gas expulsion) has been replaced by a more general model, in which star formation takes place across the full density spectrum of the ISM and only the highest-density peaks reach the star formation efficiencies necessary to become a bound cluster. While the implications of this model are that both the fraction of star formation occurring in bound clusters and the maximum cluster mass depend on the galactic environment, the underlying physics are universal. The same applies to the destruction of stellar clusters, which is now known to be dominated by tidal interactions with dense gas structures in the natal galaxy disc, rather than internal processes such as gas expulsion or evaporation. I will discuss these developments and present new observational tests of these ideas, from the Central Molecular Zone of the Milky Way to nearby dwarf, spiral, and starburst galaxies. The good agreement between theory and observations motivates an application to cluster formation and destruction across cosmic time. I will present a new model that considers the local-Universe physics of cluster formation and destruction in the context of galaxy formation, demonstrating that globular clusters are the natural outcome of regular star and cluster formation in ‘normal’ high-redshift galaxies. This unified model for cluster formation across cosmic time provides important constraints for scenarios aiming to explain the multiple stellar populations in globular clusters, and makes strong predictions for upcoming observations by ALMA, Gaia, JWST and the E-ELT.