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.1 In this article we will mainly consider non-abelian Yang-Mills theories as the example of gauge theories, but the same analysis can be repeated verbatim also in the case of the abelian electrodynamics.