Theoretical simulations and ultrafast pump-probe laser spectroscopy experiments were used to study photosynthetic pigment-protein complexes and antennae found in green sulfur bacteria such as Prosthecochloris aestuarii, Chloroflexus aurantiacus, and Chlorobium tepidum. The work focused on understanding structure-function relationships in energy transfer processes in these complexes through experiments and trying to model that data as we tested our theoretical assumptions with calculations;Theoretical exciton calculations on tubular pigment aggregates yield electronic absorption spectra that are superimpositions of linear J-aggregate spectra. The electronic spectroscopy of BChl c/d/e antennae in light harvesting chlorosomes from Chloroflexus aurantiacus differs considerably from J-aggregate spectra. Strong symmetry breaking is needed if we hope to simulate the absorption spectra of the BChl c antenna;The theory for simulating absorption difference spectra in strongly coupled photosynthetic antenna is described, first for a relatively simple heterodimer, then for the general N-pigment system. The theory is applied to the Fenna-Matthews-Olson (FMO) BChl a protein trimers from Prosthecochloris aestuarii and then compared with experimental low-temperature absorption difference spectra of FMO trimers from Chlorobium tepidum;Circular dichroism spectra of the FMO trimer are unusually sensitive to diagonal energy disorder. Substantial differences occur between CD spectra in exciton simulations performed with and without realistic inhomogeneous distribution functions for the input pigment diagonal energies. Anisotropic absorption difference spectroscopy measurements are less consistent with 21-pigment trimer simulations than 7-pigment monomer simulations which assume that the laser-prepared states are localized within a subunit of the trimer. Experimental anisotropies from real samples likely arise from statistical averaging over states with diagonal energies shifted by inhomogeneous broadening and as such, are quite sensitive to diagonal energy disorder;The experimental anisotropies exhibit strong oscillations with ~220 fs period for certain wavelengths in one-color absorption difference experiments. The oscillations only appear when the laser pulse spectrum overlaps both of the lowest-energy groups of exciton levels clustered near 815 and 825 nm. Results suggest that the oscillations stem from quantum beating between exciton levels, rather than from coherent nuclear motion.