Evaporation of a binary mixture pool or droplet is a highly dynamic and complex process with flow driven by the presence of thermal and solutal Marangoni stresses. Experiments on ethanol/water drops have identified chaotic regimes on both the surface and interior of the droplet, while mixture composition has also been seen to govern drop wettability. Using both DNS and lubrication-type approaches, we present models for the evaporation of a binary mixture liquid pool and an axisymmetric binary droplet deposited on a heated substrate. For both cases we assume liquid surface tension is linearly dependent on both temperature and concentration while mixture properties such as viscosity also vary locally with concentration. In the case of the pool we consider a rectangular domain with a horizontal temperature gradient and use DNS to solve the governing equations. The Volume-of-Fluid method is used to account for the deformable liquid-gas interface. Systems with low Prandtl number (Pr < 1) are focused on and we examine the solutal effects arising from the introduction of the second component. For the drop we consider a thin profile with a moving contact line, taking also into account the commonly ignored effects of inertia which drives interfacial instability. We derive evolution equations and explore the dimensionless parameter space to examine the resultant effects on drop wetting and evaporation where we find qualitative agreement with experiments in both these areas.