Carbon is one of the most fascinating elements. It forms a variety of structures including the well-known diamond, graphite, vitreous carbons, and the recently discovered fullerenes and nanotubes. These allotropes present challenges in understanding the physics of wide gap insulators, lower-dimension systems and molecular solids. A new branch of materials physics has also been established, by doping graphite and fullerenes with electron donors and acceptors to form graphite intercalation compounds and fulleride salts respectively. The charge-transfer between interstitial dopant and carbon host results in profound changes in physical properties, most dramatically the creation of new superconductors from non-superconducting constituents. I will summarize the properties of these carbon allotropes and their intercalation compounds, with emphasis on crystal structure and lattice/molecular dynamics. To illustrate their potential applications, I will highlight the latest developments in disordered carbon anodes in Li-ion rechargeable battery technology.