In this paper we review the calculations that are needed to obtain the
bosonic and fermionic effective potential at finite temperature and volume (at
one loop). The calculations at finite volume correspond to $S^1\times R^d$
topology. These calculations appear in the calculation of the Casimir energy
and of the effective potential of extra dimensional theories. In the case of
finite volume corrections we impose twisted boundary conditions and obtain
semi-analytic results. We mainly focus in the details and validity of the
results.