  We explore a $C$-theorem in defect conformal field theories (DCFTs) that
unify all the known conjectures and theorems until now. We examine as a
candidate $C$-function the additional contributions from conformal defects to
the sphere free energy and the entanglement entropy across a sphere in a number
of examples including holographic models. We find the two quantities are
equivalent, when suitably regularized, for codimension-one defects (or
boundaries), but differ by a universal constant term otherwise. Moreover, we
find in a few field theoretic examples that the sphere free energy decreases
but the entanglement entropy increases along a certain renormalization group
(RG) flow triggered by a defect localized perturbation which is assumed to have
a trivial IR fixed point without defects. We hence propose a $C$-theorem in
DCFTs stating that the increment of the regularized sphere free energy due to
the defect does not increase under any defect RG flow. We also provide a proof
of our proposal in several holographic models of defect RG flows.
