CONTENTS 1. Introduction 4745 2. Classification of Carbon Nanoallotropes: Structural Description and Characterization 4746 2.1. 0D Carbon Nanoallotropes 4746 2.1.1.Fullerenes and Onion-like Carbon 4746 2.1.2. Carbon Dots 4747 2.1.3. Graphene Quantum Dots 4748 2.1.4. Nanodiamonds 4749 2.2. 1D Carbon Nanoallotropes 4749 2.2.1. Carbon Nanotubes and Nanofibers 4749 2.2.2. Carbon Nanohorns 4750 2.3. 2D Carbon Nanoallotropes 4751 2.3.1. Graphene 4751 2.3.2. Multilayer Graphitic Nanosheets 4752 2.3.3. Graphene Nanoribbons 4754 3. Methods for Preparing Carbon Nanostructures 4754 3.1. 0D Carbon Nanoallotropes 4754 3.1.1. Fullerenes and Onion-like Carbon 4754 3.1.2. Carbon Dots 4755 3.1.3. Graphene Quantum Dots 4757 3.1.4. Nanodiamonds 4760 3.2. 1D Carbon Nanoallotropes 4761 3.2.1. Carbon Nanotubes and Nanofibers 4761 3.2.2. Carbon Nanohorns 4762 3.3. 2D Carbon Nanoallotropes 4762 3.3.1. Graphene 4762 3.3.2. Multilayer Graphitic Nanosheets 4763 3.3.3. Graphene Nanoribbons 4763 4. Fundamental Physicochemical Properties of Carbon Nanoallotropes 4764 4.1. Fundamental Properties of C 60 4764 4.2. Photoluminescence of Carbon Dots and Graphene Quantum Dots 4.3. Fundamental Properties of Nanodiamonds 4.4. Mechanical Properties of Graphene, Carbon Nanotubes, and Carbon Nanofibers 4.5. Electronic and Related Properties of Graphene, Graphene Nanoribbons, Carbon Nanotubes, and Carbon Nanohorns 4.6. Magnetic Properties of Carbon Nanoallotropes 4.7. Chemical Reactivity 4.7.1. Addition to sp 2 Carbon Atoms 4.7.2. Reactions at Edges and Defect Sites 4.7.3. Noncovalent Surface Interactions 4.7.4. Internal Spaces as Nanoreactors 5. Interconversions of Carbon Nanoallotropes 6.