  Spacetime---the union of space and time---is both the actor and the stage
during physical processes in our fascinating Universe. In Lorentz invariant
local theories, the existence of a maximum signalling speed (the "speed of
light") determines a notion of causality in spacetime, distinguishing the past
from the future, and the cause from the effect. This thesis is dedicated to the
study of \emph{deviations} from locality. Focussing on a particular class of
\emph{non-local} theories that is both Lorentz invariant and free of ghosts, we
aim to understand the effects of such non-local physics in both gravity and
quantum theory. Non-local ghost-free theories are accompanied by a parameter
$\ell$ of dimension length that parametrizes the scale of non-locality, and for
that reason we strive to express all effects of non-locality in terms of this
symbol. In the limiting case of $\ell=0$ one recovers the local theory, and the
effects of non-locality vanish. In order to address these questions we develop
the notion of non-local Green functions [...]. The results presented in this
thesis establish several effects of a Lorentz invariant, ghost-free
non-locality in the areas of both gravitational and quantum physics. (Full
abstract in document.)
