  Environmental effects have an important influence on cluster galaxies, but
studies at very faint magnitudes (R>21) are almost exclusively based on
imaging. We present here a very deep spectroscopic survey of galaxies on the
line of sight to Coma, based on redshifts obtained with VLT/VIMOS for 715
galaxies in the unprecedented magnitude range 21<R<23 (absolute magnitude -14
to -12). We confirm the substructures previously identified in Coma by Adami et
al. (2005a), and identify three new ones. We detect many groups behind Coma: a
large structure at z~0.5, the SDSS Great Wall, and a large and very young
structure at z~0.054. These structures account for the mass maps derived from a
recent weak lensing analysis by Gavazzi et al. (2009). The orbits of dwarf
galaxies are probably anisotropic and radial, and could originate from field
galaxies radially falling into the cluster. Spectral characteristics of Coma
dwarf galaxies show that red or absorption line galaxies have larger stellar
masses and are older than blue or emission line galaxies. R<22 galaxies show
less prominent absorption lines than R>22 galaxies. This trend is less clear
for field galaxies, suggesting that part of the faint Coma galaxies could have
been recently injected from the field following the NGC 4911 group infall. We
present a list of five Ultra Compact Dwarf galaxy candidates. We also globally
confirm spectroscopically our previous results on the galaxy luminosity
functions and find that dwarf galaxies follow a red sequence similar to that
drawn by bright galaxies. Dwarf galaxies are very abundant in Coma, and are
partly field galaxies that have fallen onto the cluster along filaments.
