  The survey of the mid-infrared sky by the Wide-field Infrared Survey Explorer
(WISE) led to the discovery of extremely cold low-mass brown dwarfs, classified
as Y dwarfs, which extend the T class to lower temperatures. Twenty-four Y
dwarfs are known at the time of writing. Here we present improved parallaxes
for four of these, determined using Spitzer images. We give new photometry for
four late-type T and three Y dwarfs, and new spectra of three Y dwarfs,
obtained at Gemini Observatory. We also present previously unpublished
photometry taken from HST, ESO, Spitzer and WISE archives of 11 late-type T and
9 Y dwarfs. The near-infrared data are put on to the same photometric system,
forming a homogeneous data set for the coolest brown dwarfs. We compare recent
models to our photometric and spectroscopic data set. We confirm that
non-equilibrium atmospheric chemistry is important for these objects.
Non-equilibrium cloud-free models reproduce well the near-infrared spectra and
mid-infrared photometry for the warmer Y dwarfs with 425 <= T_eff K <= 450. A
small amount of cloud cover may improve the model fits in the near-infrared for
the Y dwarfs with 325 <= T_eff K <= 375. Neither cloudy nor cloud-free models
reproduce the near-infrared photometry for the T_eff = 250 K Y dwarf W0855. We
use the mid-infrared region, where most of the flux originates, to constrain
our models of W0855. We find that W0855 likely has a mass of 1.5 - 8 Jupiter
masses and an age of 0.3 - 6 Gyr. The Y dwarfs with measured parallaxes are
within 20 pc of the Sun and have tangential velocities typical of the thin
disk. The metallicities and ages we derive for the sample are generally
solar-like. We estimate that the known Y dwarfs are 3 to 20 Jupiter-mass
objects with ages of 0.6 to 8.5 Gyr.
