  This paper contains a collection of essays on nonlocal phenomena in quantum
field theory, gravity and cosmology. Mechanisms of nonlocal contributions to
the quantum effective action are discussed within the covariant perturbation
expansion in field strengths and spacetime curvatures and the nonperturbative
method based on the late time asymptotics of the heat kernel. Euclidean version
of the Schwinger-Keldysh technique for quantum expectation values is presented
as a special rule of obtaining the nonlocal effective equations of motion for
the mean quantum field from the Euclidean effective action. This rule is
applied to a new model of ghost free nonlocal cosmology which can generate the
de Sitter stage of cosmological evolution at an arbitrary value of $\varLambda$
-- a model of dark energy with its scale played by the dynamical variable that
can be fixed by a kind of a scaling symmetry breaking mechanism. This model is
shown to interpolate between the superhorizon phase of gravity theory mediated
by a scalar mode and the short distance general relativistic limit in a special
frame which is related by a nonlocal conformal transformation to the original
metric. The role of compactness and regularity of spacetime in the Euclidean
version of the Schwinger-Keldysh technique is discussed.
