What is the shape of a droplet? Its interfacial tension dictates that it is very close to a perfect sphere. Herein, the interfacial tension is reduced to ultralow values (0.1 - 100 uN/m) by careful formulation of surfactant additives, such as for mixtures that form microemulsions. The droplet need not be spherical but can accommodate external forces of a similar magnitude. The control and precision of forces afforded simply by light - in the form of highly focused Nd:YAG laser beams - are exploited in this work to deform hydrocarbon oil-in-water emulsion droplets of 1-10 um diameter. To this end, a novel, integrated platform for microfluidic generation, optical deformation and 3D fluorescent imaging of droplets is presented. Previous attempts to characterise optically-controlled microdroplet shapes have been limited to 2D projections. Here, that ambiguity is resolved using 3D confocal laser scanning- and structured illumination microscopy. 2D and 3D arrays of up to four Gaussian point traps are generated by holograms and acousto-optics. A variety of regular, prolate, oblate and asymmetric shapes are produced and correlated with parameters such as optocapillary number, trap separation and capillary length. Exotic shapes exhibiting zero or negative mean and Gaussian curvatures are presented alongside their brightfield counterparts. The complex phase behaviour of emulsion droplets and their parent phases is observed to couple strongly to thermal absorption of the beams. The rich interfacial chemistry, its relation to the forces determining droplet shape and the surprising ability to create nanofluidic networks between droplets are investigated.