Polymers consisting of amino acid building blocks continue to receive consideration for biomedical applications. Since poly(amino acid)s are built from natural amino acids, the same building blocks proteins are made of, they are biocompatible, biodegradable and their degradation products are metabolizable. Some amino acids display a unique asymmetrical AB2 structure, which facilitates their ability to form branched structures. This review compares the three forms of highly branched polymeric structures: structurally highly organized dendrimers, dendrigrafts and the less organized, but readily synthesizable hyperbranched polymers. Their syntheses are reviewed and compared, methods of synthesis modulations are considered and variations on their traditional syntheses are shown. The potential use of highly branched polymers in the realm of biomedical applications is discussed, specifically their applications as delivery vehicles for genes and drugs and their use as antiviral compounds. Of the twenty essential amino acids, L-lysine, L-glutamic acid, and L-aspartic acid are asymmetrical AB2 molecules, but the bulk of the research into highly branched poly(amino acid)s has focused on the polycationic poly(L-lysine) with a lesser extent on poly(L-glutamic acid). Hence, the majority of potential applications lies in delivery systems for nucleic acids and this review examines and compares how these three types of highly branched polymers function as non-viral gene delivery vectors. When considering drug delivery systems, the small size of these highly branched polymers is advantageous for the delivery of inhalable drug. Even though highly branched polymers, in particular dendrimers, have been studied for more than 40 years for the delivery of genes and drugs, they have not translated in large scale into the clinic except for promising antiviral applications that have been commercialized.