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The dust-to-stellar mass ratio ($M_{\rm dust}$/$M_{\rm \star}$) is a crucialyet poorly constrained quantity to understand the production mechanisms ofdust, metals and stars in galaxy evolution. In this work we explore andinterpret the nature of $M_{\rm dust}$/$M_{\rm \star}$ in 300 massive($M_{\star}>10^{10}M_{\odot}$), dusty star-forming galaxies detected with ALMAup to $z\approx5$. We find that $M_{\rm dust}$/$M_{\rm \star}$ evolves withredshift, stellar mass, specific SFR and integrated dust size, differently formain sequence and starburst galaxies. In both galaxy populations $M_{\rmdust}$/$M_{\rm \star}$ rises until $z\sim2$ followed by a roughly flat trendtowards higher redshifts. We show that the inverse relation between $M_{\rmdust}$/$M_{\rm \star}$ and $M_{\star}$ holds up to $z\approx5$ and can beinterpreted as an evolutionary transition from early to late starburst phases.We demonstrate that $M_{\rm dust}$/$M_{\rm \star}$ in starbursts mirrors theincrease in molecular gas fraction with redshift, and is enhanced in objectswith the most compact dusty star-formation. The state-of-the-art cosmologicalsimulation SIMBA broadly matches the evolution of $M_{\rm dust}$/$M_{\rm\star}$ in main sequence galaxies, but underestimates it in starbursts. Thelatter is found to be linked to lower gas-phase metallicities and longer dustgrowth timescales relative to data. Our data are well reproduced by analyticalmodel that includes recipes for rapid metal enrichment, strongly suggestingthat high $M_{\rm dust}$/$M_{\rm \star}$ is due to fast grain growth in metalenriched ISM. Our work highlights multifold benefits of using $M_{\rmdust}$/$M_{\rm \star}$ as a diagnostic tool for: (1) separating main sequenceand starburst galaxies until $z\sim5$; (2) probing the evolutionary phases ofdusty galaxies, and (3) refining the treatment of dust life cycle insimulations.

Knocking on giants' doors: I. The evolution of the dust-to-stellar mass ratio in distant dusty galaxies