It remains a major challenge to derive a theory of cloud-scale ($\lesssim100$ pc) star formation and feedback, describing how galaxies convert gas into stars as a function of the galactic environment. Progress has been hampered by a lack of robust empirical constraints on the giant molecular cloud (GMC) lifecycle. We address this problem by systematically applying a new statistical method for measuring the evolutionary timeline of the GMC lifecycle, star formation, and feedback to a sample of nine nearby disc galaxies, observed as part of the PHANGS-ALMA survey. We measure the spatially-resolved ($\sim100$ pc) CO-to-H$\alpha$ flux ratio and find a universal de-correlation between molecular gas and young stars on GMC scales, allowing us to quantify the underlying evolutionary timeline. GMC lifetimes are short, typically 10-30 Myr, and exhibit environmental variation, between and within galaxies. At kpc-scale molecular gas surface densities $\Sigma_{\rm H_2}\geqslant8$M$_{\odot}$pc$^{-2}$, the GMC lifetime correlates with time-scales for galactic dynamical processes, whereas at $\Sigma_{\rm H_2}\leqslant8$M$_{\odot}$pc$^{-2}$ GMCs decouple from galactic dynamics and live for an internal dynamical time-scale. After a long inert phase without massive star formation traced by H$\alpha$ (75-90% of the cloud lifetime), GMCs disperse within just 1-5 Myr once massive stars emerge. The dispersal is most likely due to early stellar feedback, causing GMCs to achieve integrated star formation efficiencies of 4-10% These results show that galactic star formation is governed by cloud-scale, environmentally-dependent, dynamical processes driving rapid evolutionary cycling. GMCs and HII regions are the fundamental units undergoing these lifecycles, with mean separations of 100-300 pc in star-forming discs. Future work should characterise the multi-scale physics and mass flows driving these lifecycles.

The lifecycle of molecular clouds in nearby star-forming disc galaxies