  Despite the theory of neutrino oscillations being rather old, some of its
basic issues are still being debated in the literature. We discuss, in the
framework of the wave packet approach, a number of such issues, including the
relevance of the "same energy" and "same momentum" assumptions, the role of
quantum-mechanical uncertainty relations in neutrino oscillations, the
dependence of the production/detection and propagation coherence conditions
that ensure the observability of neutrino oscillations on neutrino energy and
momentum uncertainties, the question of (in)dependence of the oscillation
probabilities on the neutrino production and detection processes, the
applicability limits of the stationary source approximation, and Lorentz
invariance of the oscillation probability. We also develop a novel approach to
calculation of the oscillation probability in the wave packet picture, based on
the summation/integration conventions different from the standard one, which
gives a new insight into the oscillation phenomenology. We discuss a number of
apparently paradoxical features of the theory of neutrino oscillations.
