The fullerene era was started in 1985 with the discovery of the stable C 60 cluster and its interpretation as a cage structure with the familiar shape of a soccer ball [1]. An explosive growth in fullerene research was triggered in 1990 by the development of a method to produce fullerenes in bulk quantities [2]. Subsequently, the structural, electronic, and vibrational properties of many fullerenes have been studied in detail. The importance and potential of this new class of materials is exemplified by the discovery of intermediatetemperature superconductivity in doped C 60 [3]. Carbon nanotubes, a novel form of carbon which combines the properties of graphite and fullerenes, were discovered in 1991 [4]. Because of their intriguing properties and potential for applications, nanotubes are currently the subject of very intense research. Polymerization of C 60 molecules, particularly by photoexcitation [5] but by several other techniques as well, also results in a variety of interesting new structures, which contain both 4-coordinated and 3-coordinated carbon atoms [6]. The burgeoning field of fullerene research has been reviewed by several authors [7][8][9][10][11][12], most notably by Dresselhaus et al. [11] in an extensive monograph that appeared in 1996.In spite of the rapidly increasing interest in new forms of fullerenes, icosahedral C 60 , the "most beautiful molecule" [13], remains the focus of vigorous research as the prototype fullerene system. The present chapter concerns the vibrational structure of C 60 and the efforts to unravel its details using spectroscopic techniques. This remains a work in progress, but we hope to show that a look at the existing body of experimental and theoretical research from the broader perspective of an extended article provides a deeper understanding of the vibrational properties of C 60 .