  Nonunitarity can arise in neutrino oscillation when the matrix with elements
$\mathbf{U}_{\alpha i}$ which relate the neutrino flavor $\alpha$ and mass $i$
eigenstates is not unitary when sum over the kinematically accessible mass
eigenstates or over the three Standard Model flavors. We review how high scale
nonunitarity arises after integrating out new physics which is not accessible
in neutrino oscillation experiments. In particular, we stress that high scale
unitarity violation is only apparent and what happens is that the neutrino
flavor states become nonorthogonal due to new physics. Since the flavor space
is complete, unitarity has to be preserved in time evolution and that the
probabilities of a flavor state oscillates to all possible flavor states always
sum up to unity. We highlight the need to modify the expression of probability
to preserve unitarity when the flavor states are nonorthogonal. We will
continue to call this high scale unitarity violation in reference to a
nonunitary $\mathbf{U}$. We contrast this to the low scale nonunitarity
scenario in which there are new states accessible in neutrino oscillation
experiments but the oscillations involving these states are fast enough such
that they are averaged out. We further derive analytical formula for the
neutrino oscillation amplitude involving $N$ neutrino flavors without assuming
a unitarity $\mathbf{U}$ which allows us to prove a theorem that if
$\left(\mathbf{U}\mathbf{U}^{\dagger}\right)_{\alpha\beta}=0$ for all
$\alpha\neq\beta$, then the neutrino oscillation probability in an arbitrary
matter potential is indistinguishable from the unitarity scenario.
Independently of matter potential, while nonunitarity effects for high scale
nonunitarity scenario disappear as
$\left(\mathbf{U}\mathbf{U}^{\dagger}\right)_{\alpha\beta}\to 0$ for all
$\alpha\neq\beta$, low scale nonunitarity effects can remain.
