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The original cosmological models assumed a Universe that underwent deceleration during its entire evolution, corresponding to the slowing of the expansion through gravitational deceleration. As cosmology has developed, this assumption has been overturned at two separate epochs. It is now widely believed that the Universe underwent a phase of accelerated expansion, known as cosmological inflation, during some early stage of the Universe's expansion. This hypothesis provides what is currently the best explanation for the observed structures in the Universe, especially cosmic microwave background anisotropies. In the present Universe evidence from many types of observation, most prominently the apparent magnitude-redshift relation of distant type Ia supernovae, suggests that the Universe is presently accelerating, which can be explained by the existence of a cosmological constant or an unusual form of matter sharing similar properties, often referred to as quintessence.

The purpose of this article is to provide an introductory review of these two topics, highlighting the ways in which the two phenomena may be a consequence of the same underlying physical mechanism - domination of the Universe by the energy density of a scalar field. It begins with an overview of inflation in the early Universe, with the focus very much directed towards inflation as a theory of the origin of structure. This is a particularly exciting time for proponents of this mechanism, as microwave anisotropy measurements from the BOOMERanG and MAXIMA experiments [1, 2] have given strong support to its basic predictions, opening the possibility of high-precision testing in the future. Later in the article, the current status of understanding of the present acceleration in the context of scalar field domination is discussed, and challenges and unsolved problems highlighted.