Studies of sessile droplets provide a natural framework for modeling dynamic contact lines. We present several recent results on droplet behavior on heated substrates under the conditions when the effects of both wetting and evaporation are important. For liquids which are aqueous solutions, we investigate how the formation of electrical double layers near the interfaces affects droplet spreading and evaporation. Apparent contact angle is found as a function of both heating and ion concentration in the liquid. For non-polar organic liquids we focus on recent advances in modeling of processes in the gas phase for the case of diffusion-limited evaporation. We present numerical results on how diffusion in the moist air affects droplet behavior and identify Stefan flow as an important contributor to the heat and mass transfer near contact lines. A method for finding the local Stefan flow velocity from the experimental data on trajectories of microdroplets flying over a contact line is proposed.