Life on earth is based on compounds that have carbon frames and backbones. Today, chemists have added to the world of biomolecules and biopolymers approximately 107 different synthetic molecules and polymers, the structures of which also depend on the formation of strong, stable carbon–carbon bonds. Although the stability of carbon–carbon bonds has been recognized for more than a century, the two natural modifications graphite and diamond were, until recently, the only allotropic forms of carbon on earth that were available in macroscopic quantities and were structurally well characterized. With the synthesis of macroscopic quantities of buckminsterfullerene (C60) and the higher fullerenes (C70, C76, C78, etc.) and the exploration of the fascinating properties of these all-carbon spheres, this situation has completely changed. In the coming decades, the design, preparation, and study of novel molecular and polymeric allotropic forms of carbon will be a central topic in chemistry. Research in this area will dramatically advance the fundamental knowledge on carbon-based matter and, as already illustrated by the ongoing work on C60, generate unprecedented technological perspectives. This review surveys synthetic organic-chemical approaches toward the preparation and study of all-carbon molecules and polymers that differ from the familiar networks of graphite and diamond as well as from the fullerenes. We will also discuss the ongoing research on fullerenes with a particular focus on the synthetic approaches to these all-carbon spheres and their transition metal complexes.