  Mapping the molecular gas content of the universe is key to our understanding
of the build-up of galaxies over cosmic time. Spectral line scans in deep
fields, such as the Hubble Ultra Deep Field (HUDF), provide a unique view on
the cold gas content out to high redshift. By conducting
`spectroscopy-of-everything', these flux-limited observations are sensitive to
the molecular gas in galaxies without preselection, revealing the cold gas
content of galaxies that would not be selected in traditional studies. In order
to capitalize on the molecular gas observations, knowledge about the physical
conditions of the galaxies detected in molecular gas, such as their
interstellar medium conditions, is key. Fortunately, deep surveys with
integral-field spectrographs are providing an unprecedented view of the galaxy
population, providing redshifts and measurements of restframe UV/optical lines
for thousands of galaxies. We present the results from the synergy between the
ALMA Spectroscopic Survey of the HUDF (ASPECS), with deep integral field
spectroscopy from the MUSE HUDF survey and multi-wavelength data. We discuss
the nature of the galaxies detected in molecular gas without preselection and
their physical properties, such as star formation rate and metallicity. We show
how the combination of ALMA and MUSE integral field spectroscopy can constrain
the physical properties in galaxies located around the main sequence during the
peak of galaxy formation.
