The effect of physical compatibilization on the deformation and coalescence of droplets in immiscible polymer blends is discussed. Evidence is provided for the existence of concentration gradients in block copolymers along the interface during deformation. This causes complex changes in droplet shapes during deformation and relaxation. These concentration gradients also result in Marangoni stresses, which stabilize the droplets against deformation and breakup. Coalescence experiments have been performed, varying both the compatibilizer concentration and the shear rate. Existing coalescence models have been evaluated. An empirical extension of Chesters' partially mobile interface model is presented, that treats the effects of Marangoni stresses on the coalescence process as a higher effective viscosity ratio.