The evaporation of a liquid droplet on a solid substrate is a ubiquitous physical phenomenon. In a vast variety of real-life situations spherical drops are the exception rather than the rule, yet the intricacy of the physical mechanisms involved has constrained the study of this problem to spherical configurations. In this talk, we revisit milestone investigations dealing with the evaporation kinetics, bulk flow, thermocapillary stability, and binary-mixture dynamics of small spherical sessile drops and extend their scope to the largely unexplored case of non-spherical geometries. Through a combination of experiments and numerical simulations we illustrate a number of new geometry-induced effects, which demonstrates the substantial loss of physical richness accompanying the simplifying axisymmetric assumption. We also present a universal scaling law for the diffusion-limited evaporation rate of any drop shape.