We will present recent work on two biomedical examples of protein aggregation from aqueous solutions. The first is a model that can predict the formation of a fractal network of insulin monomers and the subsequent break-up of the fractal network into microspherical aggregates. The results of our study capture the main features of a recent experimental study of insulin microcrystal precipitation. The second is a theoretical calculation of the critical bundle size of sickle hemoglobin chains. The formation of these bundles is thought to be the crucial kinetic process that leads to sickle cell anemia.