  I review a class of nonlocally modified gravity models which were proposed to
explain the current phase of cosmic acceleration without dark energy. Among the
topics considered are deriving causal and conserved field equations, adjusting
the model to make it support a given expansion history, why these models do not
require an elaborate screening mechanism to evade solar system tests, degrees
of freedom and kinetic stability, and the negative verdict of structure
formation. Although these simple models are not consistent with data on the
growth of cosmic structures many of their features are likely to carry over to
more complicated models which are in better agreement with the data.
