This review discusses the development of functional and multifunctional dendrimeric and hyperbranched polymers, collectively called dendritic polymers, with the objective of being applied as drug and gene delivery systems. In particular, using as starting materials known and well-characterized basic dendritic polymers, the review deals with the type of structural modifications to which these dendritic polymers were subjected for the development of drug carriers with low toxicity, high encapsulating capacity, a specificity for certain biological cells, and the ability to be transported through their membranes. Proceeding from functional to multifunctional dendritic polymers, one is able to prepare products that fulfill one or more of these requirements, which an effective drug carrier should exhibit. A common feature of the dendritic polymers is the exhibition of polyvalent interactions, while for multifunctional derivatives, a number of targeting ligands determine specificity, another type of group secures stability in biological milieu and prolonged circulation, while others facilitate their transport through cell membranes. Furthermore, dendritic polymers employed for gene delivery should be or become cationic in the biological environment for the formation of complexes with the negatively charged genetic material.