  We compute the Compton scattering off the nucleons in the framework of
manifestly covariant baryon chiral perturbation theory (B$\chi$PT). The results
for observables differ substantially from the corresponding calculations in
heavy-baryon chiral perturbation theory (HB$\chi$PT), most appreciably in the
forward kinematics. We verify that the covariant $p^3$ result fulfills the
forward-Compton-scattering sum rules. We also explore the effect of the
$\Delta$(1232) resonance at order $p^4/\varDelta$, with $\varDelta\approx 300$
MeV, the resonance excitation energy. We find that the substantial effect of
the $\Delta$-excitation on the nucleon polarizabilities can naturally be
accommodated in the manifestly covariant calculation.
