Correlated electron-hole pairs, or excitons, in semiconductor nanostructures have been studied over the past few decades. The optical response of excitons is complicated due to inhomogeneous broadening, presence of multiple states, and exciton-exciton interactions. In this work we bring new perspectives to exciton physics in semiconductor quantum wells (QWs) through two-dimensional coherent spectroscopy. We have studied the polarization-dependent exciton dephasing rate in low-symmetry structures, which depends on the crystal-axis-dependent absorption coefficient. Our experiments on the spectral diffusion of excitons highlight the limitations of previously used models at low sample temperatures. Finally, we have developed an intuitive and simple model to include exciton-exciton interactions by treating excitons as interacting bosons. We quantify these interactions using a numerical fitting procedure.