  It is well known that standard gauge theories are renormalizable in D=4 while
Einstein gravity is renormalizable in D=2. This is where the research in the
field of two derivatives theories is currently standing. We hereby present a
class of weakly non-local higher derivative gravitational and gauge theories
universally consistent at quantum level in any spacetime dimension. These
theories are unitary (ghost-free) and perturbatively renormalizable. Moreover,
we can always find a simple extension of these theories that is
super-renormalizable or finite at quantum level in even and odd spacetime
dimensions. Finally, we propose a super-renormalizable or finite theory for
gravity coupled to matter laying the groundwork for a "finite standard model of
particle physics" and/or a grand unified theory of all fundamental
interactions.
