  We develop here the theme that extremely metal-deficient Blue Compact Dwarf
Galaxies (BCDs), those with Z < Zsun/20, are young galaxies which did not start
to form stars until ~ 100 Myr ago. They can be thus considered as primeval
galaxies in our local volume of the universe, and are excellent laboratories
for studying physical processes occuring at the time of galaxy formation in
very metal-deficient environments. We use BCDs to derive a new value of the
primordial helium abundance Yp = 0.244+/-0.001, higher than previous
determinations. This corresponds to a baryon mass fraction Omega_b*h^2_{50} =
0.058+/-0.007. We discuss the problem of dust in a very low-metallicity
environment and show how a large fraction (~ 75%) of the young stars are not
visible, and that any derivation of the cosmic star formation rate based only
on optical/UV fluxes would be an underestimate. We also show how the loss of
Ly-alpha photons from starburst regions puts strong constraints on Ly-alpha
searches of high-redshift galaxies.
