C-60 is a symbol of nanoscience. Its impact is far beyond the initial interest in this nanometer molecule itself. This paper reviews the current status of the nonlinear optical and ultrafast dynamics investigations of C-60. The review starts with the nonlinear optical response, in particular the dispersion spectra of harmonic generation and two-photon absorption. Both the experimental and theoretical challenges are highlighted. The main focus is on femtosecond and picosecond degenerate and nondegenerate four-wave mixing and pump-probe techniques as a tool to investigate ultrafast electron and nuclear dynamics, charge transfer and photoexcitation in C-60. Theoretical investigations are essential to understand these processes. Theory predicts a longer relaxation time for charge transfer than photoexcitation and reveals the underlying reasons for the normal mode excitations and changes in the electron density of states, which is directly linked to the time-resolved photoemission spectra. Theory also resolves a long-time puzzle about the dependence of normal mode excitations on the laser pulse duration and predicts that time-resolved pump-probe spectroscopy is able to probe electron correlation effects. Finally, high-harmonic generation in C-60, is reviewed. The review concludes with prospectives and possible applications.