The evaporation of non-axisymmetric sessile drops is studied by means of experiments and three-dimensional (3D) direct numerical simulations. The emergence of azimuthal currents and pairs of counter-rotating vortices in the liquid bulk flow is reported in drops with non-circular contact area. These phenomena, especially the latter which is also observed experimentally, are found to play a critical role in the transient flow dynamics and associated heat transfer. Non-circular drops exhibit variable wettability along the pinned contact-line sensitive to the choice of system parameters, and inversely dependent on the local contact-line curvature, providing a simple criterion for estimating the approximate contact-angle distribution. The evaporation rate is found to vary in the same order of magnitude as the liquid-gas interfacial area. Furthermore, the more complex case of drops evaporating with a moving contact line in the constant contact-angle mode is addressed. Interestingly, the numerical results demonstrate that the average interface temperature remains essentially constant as the drop evaporates in the constant-angle mode, while this increases in the constant-radius mode as the drops becomes thinner. It is therefore concluded that, for increasing substrate heating, the evaporation rate increases more rapidly in the constant-radius mode than in the constant-angle mode. In other words, the higher the temperature the larger the difference between the lifetimes of an evaporating drop in the constant-angle mode with respect to that evaporating in the constant-radius mode.