A surfactant-laden fluid droplet, when emplaced upon a thin film of the same fluid, spreads and dramatic fingering patterns localised at the droplet edge are seen experimentally. A long-standing question has been how these fingers arise and to deduce a mechanism for their formation. Recent theory and numerical simulation has discovered why this occurs. This talk begins by describing the analysis and this phenomenon. Other interesting, and related, phenomena such as the superspreading of droplets (that is, unusually fast spreading) and the behaviour of droplets above, and below, the critical micelle concentration are also to be discussed.