A process in which a disordered system of pre-existing molecules generates an organized structure through specific, local interactions among the molecules themselves is termed molecular self-assembly. Micelles, microemulsions, and vesicles are examples of such self-assembled systems where amphiphilic molecules are involved. As the functional properties of these systems (such as wetting and emulsification, release of solubilized drugs, etc.) are dictated by the dynamic behavior of the surfactants at the molecular level, it is of immense interest to investigate these systems for the same. The dynamics in soft matter systems is quite complex, involving different time and length scales. We used a combination of neutron scattering and molecular dynamics simulation studies in probing the dynamic landscape in various self-assembled surfactant aggregates. Neutron scattering experiments were carried out using several spectrometers covering a wide dynamic range to probe motions on different time scales. The interaction between the surfactants can be varied by changing the molecular architecture, counterion concentration, temperature, and so forth. It is important to study the effect of these parameters on the dynamics of surfactants in these aggregates. We have carried out experiments on various ionic (anionic as well as cationic) micelles with varied counterion concentrations, vesicles, and lipid bilayers to unravel the complex dynamic features present in these systems. In this feature article, we will discuss some important results of our recent work on dynamics in these self-assembled surfactant aggregates.