  We propose a gauge-invariant description for the Higgs mechanism by which a
gauge boson acquires the mass. We do not need to assume spontaneous breakdown
of gauge symmetry signaled by a non-vanishing vacuum expectation value of the
scalar field. In fact, we give a manifestly gauge-invariant description of the
Higgs mechanism in the operator level, which does not rely on spontaneous
symmetry breaking. For concreteness, we discuss the gauge-Higgs models with
$U(1)$ and $SU(2)$ gauge groups explicitly. This enables us to discuss the
confinement-Higgs complementarity from a new perspective.
