  Quantum optics with giant emitters has shown a new route for the observation
and manipulation of non-Markovian properties in waveguide-QED. In this paper we
extend the theory of giant atoms, hitherto restricted to the perturbative
light-matter regime, to deal with the ultrastrong coupling regime. Using static
and dynamical polaron methods we address the low energy subspace of a giant
atom coupled to an Ohmic waveguide beyond the standard rotating wave
approximation. We analyze the equilibrium properties of the system by computing
the atomic frequency renormalization as a function of the coupling
characterizing the localization-delocalization quantum phase transition for a
giant atom. We show that virtual photons dressing the ground state are
non-exponentially localized around the contact points but decay as a power-law.
Dynamics of an initially excited giant atom are studied, pointing out the
effects of ultrastrong coupling on the Lamb shift and the spontaneous emission
decay rate. Finally we comment on the existence of the so-called oscillating
bound states beyond the rotating wave approximation.
