VISUALS Sketch of the main constituents of galaxies. Stars (1) form out of the dense molecular gas reservoir (2). At low densities, gas reservoirs are mostly atomic (3). Galaxies reside in halos where gas is hot and ionized (4). The vast space between galaxies hosts the intergalactic medium which is also made up of diffuse hot gas. Each phase can be traced with observations in various bands of the electromagnetic spectrum. ASPECS helped to constrain the flow of the different gas phases towards the centres of galaxies by observing the molecular gas with ALMA.Design infographic: Daniela Leitner Most of ordinary (i.e., baryonic) matter in the Universe resides outside galaxies, in the tenuous circumgalactic and intergalactic medium. As galaxies start to form, they attract more and more matter via gravitational attraction. The content of ordinary matter in galaxies thus increases as a function of cosmic time (as indicated by the growing size of the pie charts in this figure). At the same time, the relative contribution of stars, molecular gas (mapped by ASPECS) and atomic gas within galaxies changes through cosmic history, as indicated by the pie charts in the bottom.Design infographic: Daniela Leitner The ASPECS band 3 and band 6 footprints (as indicated by the blue and green borders), compared to the Hubble Extremely Deep Field (yellow rectangle) and the original Hubble Ultra Deep Field (white square). Comparison between the Hubble optical/near-infrared image in the ASPECS footprint of the H-UDF, shown to the right. 3D renderings of the ASPECS band 3 and 6 cubes. Strong cold molecular gas emitters appear as bright spots in the cubes. Linear features correspond to bright dust-continuum sources 3D rendering of the MUSE Hubble Ultra Deep Field Survey cube, after subtraction of the continuum emission. Nebular line emission from hot gas in galaxies appears as bright spots in the cube. Optical/near-infrared image of the ASPECS field. Sources detected in the dust and in molecular gas are indicated with different symbols. Comparison between the HST imaging of a part of the ASPECS field (left), its Spitzer/Herschel map (right, in colors) and the ASPECS map (right, in white contours). Compared to previous low-resolution far-infrared measurements, the ~1 arcsec resolution ALMA imaging accurately pin-points the location of distant dusty galaxies. Hubble Space Telescope postage stamp images, shown in color scales, of the brightest molecular gas emitters in the ASPECS footprint. The overlaid contours show the molecular gas maps. This composition highlights the diversity of gas-rich galaxies in the Hubble Ultra Deep Field. By combining the sensitive ASPECS data with the exquisite redshift information from the MUSE Hubble Ultra Deep Field Survey (Bacon et al. 2017, Inami et al. 2017), the ASPECS team was able to investigate the average properties of molecular gas in samples of distant galaxies that are too faint to be detected individually. Evolution of the baryonic mass components in galaxies, averaged over cosmological volumes, as a function of cosmic time. The red line indicates the build-up of stellar mass with cosmic time. The blue line shows the molecular gas reservoir, i.e., the fuel for star formation, as measured by ASPECS. If the observed trends can be extrapolated into the future, the cosmic density of molecular gas will constantly decline, i.e., the growth in stellar mass will eventually become insignificant.