Cosmic acceleration has come to be a standard, and perhaps required, ingredient in our current understanding of the universe. In the early universe, under the name of inflation, a phase of accelerated expansion is used to solve many problems with the standard Hot Big Bang cosmology. In the late universe, cosmic acceleration seems to best explain a wide variety of observations. In both cases, we lack a complete theory of what drives cosmic acceleration. In this thesis I discuss some open issues in our understanding of cosmic acceleration, both in the early and late universe
