Dendrimer chemistry is one of the most fascinating and rapidly expanding areas of modern chemistry. This review attempts to uncover the appeal of these structurally-perfect branched macromolecules. The three intriguing regions of a dendritic molecule are discussed: the multifunctional surface, the tailored sanctuary within the branches, and the encapsulated core. The advantages of dendritic structures for property modification, and their potential applications in very diverse areas are illustrated. The exciting merger of dendrimer chemistry with self-assembly offers new, stimulating avenues for exploration. Consequently, self-assembling dendrimers comprise a major section of this article.