In this paper we summarize our experimental work on the dephasing of excitons in self-assembled InAs/GaAs quantum dots, measured using a sensitive four-wave mixing technique in heterodyne detection. Transient four-wave mixing is a powerful technique to measure not only exciton dephasing times but also fine-structure splitting energies and exciton-biexciton binding energies which are important physical parameters for the implementation of quantum dots as source of polarization-entangled photon pairs and in the design of quantum algorithms. The scope of this paper is to review and discuss, in the context of present theories and in comparison with other experiments in the literature, the most significant results of our study on a series of thermally annealed quantum dots exhibiting systematic differences in the excitonic recombination energies and quantum confinement potentials. We will highlight the main outcomes of these measurements and give a perspective in terms of open questions that still need to be investigated, possible new experiments and potential areas of interest.