  We discuss in detail the effect of neutrino oscillations in Big Bang
nucleosynthesis, between active and sterile neutrinos, as well as between
active and active neutrinos. We calculate the constraints on mixings between
active and sterile neutrinos from the present observation of the primordial
helium abundance and discuss the potential implications on various
astrophysical and cosmological problems of such oscillations. In particular, we
show that large angle sterile neutrino mixing seems to be excluded as a MSW
solution to the solar neutrino situation or a solution to the atmospheric
neutrino mixing hinted at in some underground experiments. We show how with
this constraint, the next generation of solar neutrino experiments should be
able to determine the resolution of the solar neutrino problem. It is also
shown how sterile neutrinos remain a viable dark matter candidate.
