Hyperbranched polymers are polydispersed highly branched dendritic molecules. Due to their properties, their potential for use in many applications is promising. In addition, easy synthesis and purification that is time and cost effective compared to traditional dendrimers adds to their appeal. The similarity between the structure of hyperbranched polymers and many biological systems has highlighted their importance in many biological applications. Copolymerization greatly increases the advantages associated with these polymers, making them even more suitable for use in many applications. The first part of this research project was an investigation into the effect of the degree of branching on the bulk properties and internal environment of hyperbranched polymers. In terms of the bulk properties, a viscosity study of a series of hyperbranched polymers possessing a relatively constant molecular weight and polydispersity index along with a varied degree of branching was performed. Polymers with a higher degree of branching showed relatively less viscosity than polymers with a lower degree of branching. However, the former could maintain their dendritic structure up to a degree of branching of 37%. The study also assessed the effect of the molecular weight and polydispersity index on these polymers. In the case of the internal environment, the studies were performed by measuring the binding constant of various ligands to hyperbranched polymers with a different degree of branching. The study was carried out on two different molecular weights, one below and one above the dense packing limit. The study revealed an interesting result regarding the steric and electronic effect; polymers with a low degree of branching altered their dense packing limit. For hyperbranched polymers with a molecular weight below the dense packing limit, the association constant decreased as the degree of branching decreased. However, in the case of hyperbranched polymers with a molecular weight above the dense packing limit, the association constant increased as the degree of branching decreased. Finally, a study was carried out to identify the location of comonomers within the dendritic structure. The second part of this project involved applying post synthetic methodology to copolymerise various co-monomers with hyperbranched polymers at room temperature. The use of this method to copolymerise sensitive functional units was successful. This methodology gave the dendritic system many advantages, such as improvement in the molecular weight and the degree of branching. In the final part of this project, high loaded catalytic sites hyperbranched polymers were examined to determine whether or not they could be used as a soluble catalytic support system, and it was found that they could. A solvent effect study revealed that these polymers could be used to control reactions selectivity.