The properties of dendrimers ("starburst" molecules) under varying solvent conditions are studied using molecular dynamics simulations. The dendrimers are found to have a compact (space filling) structure under all solvent conditions, with a radius of gyration which scales with the number of monomers as R(G) proportional to N-1/3. For high generation number dendrimers, there is a distinct region of constant monomer density. The density in this region depends only on the solvent quality and is independent of the generation number. When the contributions of the different generations to the overall density profile are separated, we find that the monomers which belong to the first few generations are stretched and spatially localized. Later generations are less localized and penetrate well into the central regions of the dendrimer. The different primary branches ("dendrons") of the dendrimers are found to be segregated. The amount of spatial overlap between the different dendrons decreases with increasing generation number of the dendrimer and increasing solvent quality. The relaxation times of the fluctuations of the internal structure were evaluated as well, to ensure that the simulations were run long enough for adequate sampling.