  In String Theory there often appears a rather interesting class of higher
derivative theories containing an infinite set of derivatives in the form of an
exponential. These theories may provide a way to tame ultraviolet divergences
without introducing ghost-like states. In this invited article we provide a
brief overview on the progress that has been made over the last decade to
construct such infinite derivative theories of gravity which may be able to
address the singularity problems in gravity. In the process we will also be
able to present some general results that applies to covariant torsion-free
metric theories of gravity.
