In the first half of the period of this ERC program a large number of key science goals have already been met. The focus has been on two related aspects: A) Detailed studies of the cosmic evolution of the molecular gas content through the PI-led ALMA Large Program ASPECS, and B) In-depth studies of the interstellar medium in the most distant quasar host galaxies with ALMA. For project A, significant efforts went into calibrating, reducing, and analysing the data from the first ALMA deep field: ASPECS exploits the unprecedented sensitivity of ALMA to advance our understanding of the molecular gas and dust content in distant galaxies. Targeting the iconic Hubble Ultradeep Field (UDF) with available 30-band photometry, we implemented a novel observing strategy to study the molecular gas properties in distant galaxies. Instead of targeting molecular gas emission lines in individual galaxies pre-selected through multi-wavelength observations, this approach employed a ‘spectral scanning’ method to obtain an unbiased measurement of the molecular gas content in a well-defined cosmological volume. At the same time, these spectral scans delivered the deepest-ever dust continuum maps of the universe. Taken together, these methods have allowed for a full characterisation of molecular gas and dust in the cosmological volume probed by the UDF, down to galaxy masses that encompass the bulk of the luminosity and masses out to redshifts ~4, i.e. when the Universe was only 1/7th of today’s age. A number of key publications have already been published from this project, and the final set of papers (including the ‘summary’ paper on the cosmic baryon cycle by the PI) will be published later this year. For project B, we have pushed ALMA to obtain key measurements of the interstellar medium of some of the most extreme objects in the early universe. These effort started with a highly successful survey of dust and gas in ~25 of these objects, which resulted in an almost 100% detection rate. These objects turned out to be so bright with ALMA that follow-up spatially resolved imaging is possible, which the group has subsequently pushed in a number of publications. This ultimately resulted in kpc-resolution imaging of the interstellar medium in dozens of quasar host galaxies that allow to spatially resolve the morphology and kinematics of galaxies and (in many cases) their companion galaxies. These studied culminated in the unprecedented 400pc imaging of a quasar host galaxy that is seen when the universe is less than 1Gyr old. In parallel, we have been focusing on multi-line imaging of these galaxies, and have demonstrated that the interstellar medium of the most distant host galaxy known (at redshift 7.5 when the Universe was a mere ~750 Myr old) was already highly enriched with heavy elements which poses significant constraints on early galaxy evolution models.