Charge resonance is a characteristic feature of organic molecules where electron donor (D) and acceptor (A) groups are linked by pi-conjugated bridges. Dipolar (D-pi-A), quadrupolar (D-pi-A-pi-D or A-pi-D-pi-A) or, more generally, multipolar molecules are widely studied for applications in nonlinear optics. We propose a general model for multipolar chromophores based on an essential-state description of the electronic structure, and accounting for the coupling of electrons and molecular vibrations and polar solvation coordinates. Depending on the charge distribution on the molecule, multistable potential energy surfaces are found for the ground state and/or the lowest-energy excited state. The resulting symmetry breaking shows up with important solvatochromic effects in either absorption or fluorescence spectra. The essential-state model lends itself quite naturally to describe supramolecular interactions in aggregates, crystals, or ordered films. At variance with the standard excitonic pictures, we relax the dipole approximation for electrostatic intermolecular interactions and demonstrate important excitonic shifts of dark (two-photon allowed) states for quadrupolar dyes. Moreover, bound-biexciton states are found with huge two-photon absorption.