  The advent of the Atacama Large Millimeter/submillimeter Array (ALMA) has
enabled a new era for studies of the formation and assembly of distant
galaxies. Cosmological deep field surveys with ALMA and other interferometers
have flourished in the last few years covering wide ranges of galaxy properties
and redshift, and allowing us to gain critical insights into the physical
mechanisms behind the galaxy growth. Here, we present a brief review of recent
studies that aim to characterize the interstellar medium properties of galaxies
at high redshift ($z>1$), focusing on blank-field ALMA surveys of dust
continuum and molecular line emission. In particular, we show recent results
from the ALMA Spectroscopic Survey in the Hubble Ultra Deep Field (ASPECS)
large program.
