In order to understand the collective behaviour of biological microswimmers, such as bacteria and spermatozoa, it is important to know which aspects are governed merely by the physics of the system and which aspects are biology-related. In the present study we address the mechanisms of locomotion of non-biological swimmers. We focus on artificial swimmers consisting in active droplets moving by Marangoni flow, in particular nematic liquid crystal droplets immersed in an aqueous solution containing an ionic surfactant, and self-propelled droplets driven by Belousov-Zhabotinsky (BZ) reactions. We numerically study the flow field outside and inside a single droplet, by means of a level set method, in order to account for both the deformation of the droplet and the interaction with a small number of neighbouring droplets. Further mechanisms that influence the locomotion, such as mass transport, chemical reactions and the coupling between the bulk and the surface concentration of the surfactants, are also specifically addressed.