Over the past twelve years, notable advances have occurred in a diverse range of scientific areas following the development of femtosecond optical frequency combs. Compared to a conventional laser source, the distinguishing feature of a femtosecond comb is that it provides a broadband source with well-defined phase coherence across the optical spectrum. This makes it a unique tool for spectroscopic applications, simultaneously providing high spectral resolution and broad spectral coverage. This tutorial review provides an introduction to femtosecond optical frequency combs, covering their principles of operation and examples of how they can be applied to spectroscopy. In this way it aims to demonstrate their potential as a versatile spectroscopic tool that could play a very significant role in future advances in the chemical sciences.