The concept of Fermi liquid lays a solid cornerstone to the understanding of electronic correlations in quantum matter. This ordered many-body state, entailed by the Pauli exclusion principle, rigorously organizes electrons at zero temperature in progressively higher momentum states, up to the Fermi surface... As such, it displays rigidity against perturbations, with consequences like Fermi-surface resonances manifesting themselves in longitudinal and transverse collective modes, as observed in liquid helium. However, the quest for understanding and probing Fermi-liquid collective modes in charged solid-state systems remains a challenge. In this paper I analyze the transverse shear response of neutral and charged three-dimensional Fermi liquids as a function of temperature, excitation frequency and momentum, for interactions expressed in terms of the first symmetric Landau parameter. I consider the effect of momentum-conserving quasiparticle collisions and momentum-relaxing scattering in relaxation-time approximation on the coupling between photons and Fermi-surface collective modes, thus deriving the Fermi-liquid optical conductivity and dielectric function. In the high-frequency, long-wavelength excitation regime the electrodynamic response entails two coherent and frequency-degenerate polaritons, and its spatial nonlocality is encoded by a frequency- and interaction-dependent Fermi-liquid generalized shear modulus; in the opposite high-momentum low-frequency regime anomalous skin effect takes place. I identify observable signatures of propagating shear collective modes in optical spectroscopy experiments, with applications to the surface impedance and the optical transmission of thin films. (read more)