  In this paper, we consider \emph{unbounded} weighted composition operators
acting on Fock space, and investigate some important properties of these
operators, such as $\calC$-selfadjoint (with respect to weighted composition
conjugations), Hermitian, normal, cohyponormal, and invertible. In addition,
the paper shows that unbounded normal weighted composition operators are
contained properly in the class of $\calC$-selfadjoint operators with respect
to weighted composition conjugations. The computation of the spectrum is
carried out in detail.
