Higgs Effective Field Theory (HEFT) is deployed to study elastic vector-boson scattering at the high LHC energies. The interaction is strong over most of the parameter space, with the minimal Standard Model being a remarkable exception. One-loop HEFT complemented with dispersion relations and the Equivalence Theorem leads to two different unitarization methods which produce analytical amplitudes corresponding to different approximate solutions to the dispersion relations: the Inverse Amplitude method (IAM) and the N/D method. The partial waves obtained can show poles in the second Riemann sheet whose natural interpretation is that of dynamical resonances with masses and widths depending on the starting HEFT parameters. Different unitarizations yield qualitatively, and in many cases quantitatively, very similar results. The amplitudes obtained provide realistic resonant and nonresonant cross sections to be compared with and to be used for a proper interpretation of the LHC data.