  Observations conducted over the last few decades show that the expansion of
the Universe is accelerating. In the standard model of cosmology, this
accelerated expansion is attributed to a dark energy in the form of a
cosmological constant. It is conceivable, however, for the dark energy to
exhibit mild dynamics (so that its energy density changes with time rather than
having a constant value), or for the accelerated expansion of the Universe to
be caused by some mechanism other than dark energy. In this work I will
investigate both of these possibilities by using observational data to place
constraints on the parameters of simple models of dynamical dark energy as well
as cosmological models without dark energy. I find that these data favor the
standard model while leaving some room for dynamical dark energy.
  The standard model also holds that the Universe is flat on large spatial
scales. The same observational data used to test dark energy dynamics can be
used to constrain the large-scale curvature of the Universe, and these data
generally favor spatial flatness, with some mild preference for spatial
curvature in some data combinations.
