  (abridged) Data and results from the WISH key program are summarized,
designed to provide a legacy data set to address its physics and chemistry.
WISH targeted ~80 sources along the two axes of luminosity and evolutionary
stage: from low- to high-mass protostars and from pre-stellar cores to
protoplanetary disks. Lines of H2O, HDO, OH, CO and [O I] were observed with
the HIFI and PACS instruments, complemented by molecules that probe UV, X-ray
or grain chemistry. Most of the far-infrared water emission from protostars is
found to be compact, originating from warm outflowing and shocked gas at high
density and temperature in at least two physical components. This gas is not
probed by low-J CO lines, only by J>14. Water is a significant, but not
dominant, coolant. Its abundance is universally low, of order H2O/H2=2E-6,
pointing to shock and outflow cavity models that include UV radiation at
100-1000 times the ISRF. In cold quiescent pre-stellar cores and envelopes, the
water abundance structure is accurately probed through velocity-resolved line
profiles, confirming basic chemistry networks. The gaseous HDO/H2O ratio of
0.025, much higher than that of bulk ice, is representative of the outer
photodesorbed ice layers and cold chemistry. Water abundances in the inner hot
cores are high, but with variations from 5E-6 to 2E-4. Combined analyses of
water gas and ice show that up to 50% of the oxygen budget may be missing, with
possible explanations discussed. Water vapor emission from disks is weak,
indicating that water ice is locked up in larger pebbles early on and that
these pebbles have settled and drifted inward by the Class II stage.
Quantitatively, many oceans of water ice are available. Extragalactic low-J H2O
emission is mostly compact and collisionally excited. Prospects for future mid-
to far-infrared missions are given.

Astrophysics of Galaxies;Earth and Planetary Astrophysics