Photosynthetic light harvesting is a unique life process that occurs with amazing efficiency. Since the discovery of the structure of the bacterial peripheral light-harvesting complex (LH2), this process has been studied using a variety of advanced laser spectroscopic methods. We are now in a position to discuss the physical origins of excitation energy transfer and trapping in the LH2 and LH1 antennae of photosynthetic purple bacteria. We demonstrate that the time evolution of the state created by the light is determined by the combined action of excitonic pigment-pitment interactions, energetic disorder, and coupling to nuclear motion in a pigment-protein complex. A quantitative fit of experimental data using Redfield theory allowed us to determine the pathways and time scales of exciton and vibrational relaxation and analyze separately different contributions to the measured transient absorption dynamics. Furthermore, these dynamics were observed to be strongly dependent on the excitation wavelength. A numerical fit of this dependence turns out to be extremely critical to a variation of the structure and disorder parameters and, therefore, can be used as a test for different antenna models (disordered ring, elliptical deformations, correlated disorder, etc.). The calculated equilibration dynamics in the exciton basis allow a visualization of the exciton motion using a density matrix picture in real space.