  The forward doubly-virtual Compton scattering (VVCS) off the nucleon contains
a wealth of information on nucleon structure, relevant to the calculation of
the two-photon-exchange effects in atomic spectroscopy and electron scattering.
We report on a complete next-to-leading-order (NLO) calculation of low-energy
VVCS in chiral perturbation theory ($\chi$PT). Here we focus on the unpolarized
VVCS amplitudes $T_1(\nu, Q^2)$ and $T_2(\nu, Q^2)$, and the corresponding
structure functions $F_1(x, Q^2)$ and $F_2(x,Q^2)$. Our results are confronted,
where possible, with "data-driven" dispersive evaluations of low-energy
structure quantities, such as nucleon polarizabilities. We find significant
disagreements with dispersive evaluations at very low momentum-transfer $Q$;
for example, in the slope of polarizabilities at zero momentum-transfer. By
expanding the results in powers of the inverse nucleon mass, we reproduce the
known "heavy-baryon" expressions. This serves as a check of our calculation, as
well as demonstrates the differences between the manifestly Lorentz-invariant
(B$\chi$PT) and heavy-baryon (HB$\chi$PT) frameworks.
