  We review various field theory approaches to the description of neutrino
oscillations in vacuum and external fields. First we discuss a relativistic
quantum mechanics based approach which involves the temporal evolution of
massive neutrinos. To describe the dynamics of the neutrinos system we use
exact solutions of wave equations in presence of an external field. It allows
one to exactly take into account both the characteristics of neutrinos and the
properties of an external field. In particular, we examine flavor oscillations
an vacuum and in background matter as well as spin flavor oscillations in
matter under the influence of an external electromagnetic field. Moreover we
consider the situation of hypothetical nonstandard neutrino interactions with
background fermions. In the case of ultrarelativistic particles we reproduce an
effective Hamiltonian which is used in the standard quantum mechanical approach
for the description of neutrino oscillations. The corrections to the quantum
mechanical Hamiltonian are also discussed. Then we study a spatial evolution of
mixed massive neutrinos emitted by classical sources. This method seems to be
more realistic since it predicts neutrino oscillations in space. Besides
oscillations among different neutrino flavors, we also study transitions
between particle and antiparticle states. Finally we use the quantum field
theory method, which involves virtual neutrinos propagating between production
and detection points, to describe particle-antiparticle transitions of Majorana
neutrinos in presence of background matter.
