Molecular aggregates have been of great importance in the discovery of new materials. In particular for this dissertation, we have studied the molecular aggregates of light-harvesting complexes (LHCs) and topological insulators in the form of dimer models. We address these systems on two fronts: the green sulfur bacteria bchQRU Chlorobium tepidum and the Su-Schrieffer-Heeger (SSH) model. Recently, there has been increased interest in uncovering the topological effects in and spectral properties of realistic systems. The Radiative Hamiltonian, a physically-motivated effective Hamiltonian that describes the interaction of a molecular aggregate with a radiation field, and includes long-range interactions as well as non-Hermitian contributions, allows for in-depth study into such systems. For this Hamiltonian, each individual chromophore can be modeled as a two-level system with an excitation energy and a varying dipole moment. Using the average transfer time and steady-state current as metrics of exciton transport, we have investigated transport in the simple, disordered molecular aggregate chain with and without topological properties. Ultimately, the energy dynamics and transport efficiency of the given overall system changes depending on its geometry and these simple models give insight into much larger systems.