We discuss the derivation of a low-energy effective field theory of phase (Goldstone) and amplitude (Higgs) modes of the pairing field from a microscopic theory of attractive fermions. The coupled equations for Goldstone and Higgs fields are critically analyzed in the Bardeen–Cooper–Schrieffer (BCS)-to-Bose–Einstein condensate (BEC) crossover—both in three spatial dimensions and in two spatial dimensions. The crucial role of pair fluctuations is investigated, and the beyond-mean-field Gaussian theory of the BCS–BEC crossover is compared with available experimental data of the two-dimensional ultracold Fermi superfluid.