In this article, we provide a review of the uses of asphalt from ancient to modern times and we discuss the main attempts at mathematically modeling its behavior. We start with a discussion of the various definitions for asphalt and bitumen and discuss briefly some of the many fascinating uses to which they have been put from ancient to modern times. In Section 3 we survey the various attempts at unraveling the chemical structure of asphalt. The description of its physical characteristics, the early constitutive models that have been employed to describe its mechanical response, and the numerous tests to assess its properties are dealt with in Section 4. The next section is devoted to a discussion of the aging of asphalt. In Section 6, after a cursory discussion of the more classical models for asphalt concrete, we introduce the reader to a thermodynamic framework that has been recently put into place for bodies that have multiple natural configurations and use this framework to develop a model for describing the mechanical response of asphalt concrete. We use this model to describe various experiments that have been carried out on asphalt concrete and we find that the predictions of the model agree with experiments sufficiently well. This review article cites 580 references.