Einstein's theory of general relativity (GR) has been tested to a very high precision in the infrared (IR) regime, i.e. at large distances and late times.Despite its great achievements, there are still open questions which suggest that GR is incomplete in the ultraviolet (UV) regime. From a classical point of view GR suers from the presence of black hole and cosmological singularities; while from a quantum point of view GR lacks of predictability in the UV regime, being not perturbatively renormalizable.One of the most straightforward attempt aimed to complete Einstein's GR in the ultraviolet (or short-distance) regime was to introduce quadratic curvature terms in the gravitational action besides the Einstein-Hilbert term, as for example R 2 and R µν R µν . Such an action turns out to be power counting renormalizable, but suers from the presence of a massive spin-2 ghost degree of freedom, which causes classical Hamiltonian instabilities and breaks the unitarity condition at the quantum level.Recently, it has been pointed out that a possible way to ameliorate the issue of ghost is to go beyond nite order derivative theories, and to modify the Einstein-Hilbert action by introducing dierential operators made up of innite order covariant derivatives, thus giving up the locality principle. In fact, by generalizing the Einstein-Hilbert action with quadratic curvature terms made up of nonlocal (i.e. non-polynomial) operators, one can formulate a quantum theory of gravity which is unitary and that shows an improved ultraviolet behaviour. The nonlocal dierential operators are required to be made up of exponential of entire functions in order to avoid the presence of ghost-like degrees of freedom in the graviton propagator and preserve the unitarity condition.In this Thesis, we investigate some fundamental aspect of nonlocal (innite derivative) eld theories, like causality, unitarity and renormalizability. We also show how to dene and compute scattering amplitudes for a nonlocal scalar quantum eld theory, and how they behave for a large number of interacting particles. Subsequently, we discuss the possibility to enlarge the class of symmetries under which a local Lagrangian is invariant by means the introduction of non-polynomial dierential operators. Furthermore, we move to the gravity sector. After showing how to construct a ghost-free higher derivative theory of gravity, we will nd a linearized metric solution for a (neutral and charged) point-like source, and show that it is nonsingular. By analysing all the curvature tensors one can capture and understand the physical implications due to the nonlocal nature of the gravitational interaction. In particular, the Kretschmann invariant turns out to be non-singular, while all the Weyl tensor components vanish at the origin meaning that the metric tends to be conformally-at at r = 0. Similar features can be also found in the case of a Delta Dirac distribution on a ring for which no Kerr-like singularity appears. Therefore, nonlocality can regularize singularities by smearin...