A procedure for a detailed analysis of excited states in systems of interacting chromophores is proposed. By considering the one-electron transition density matrix, a wealth of information is recovered that may be missed by manually analyzing the wave function. Not only are the position and spatial extent given, but insight into the intrinsic structure of the exciton is readily obtained as well. For example, the method can differentiate between excitonic and charge resonance interactions even in completely symmetric systems. Four examples are considered to highlight the utility of the approach: interactions between the nπ* states in a formaldehyde dimer, excimer formation in the naphthalene dimer, stacking interaction in an adenine dimer, and the excitonic band structure in a conjugated phenylenevinylene oligomer.