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In this Ph.D. thesis several topics in doubly special relativity areexplored. The starting point of this theory is very different from otherperspectives: it is not a fundamental theory, but it is considered a low energylimit of a quantum gravity theory that tries to study its possible residualelements. In particular, in doubly special relativity the Einstenian relativityprinciple is generalized, adding to the speed of light $c$ another relativisticinvariant, the Planck length $l_p$. This idea can really have possibleexperimental observations, giving place to what is known as quantum gravityphenomenology. On the other hand, doubly special relativity implies theexistence of deformed composition laws for energy and momentum, which leads toa spacetime with nonlocal ingredients, an element that also appears in otherapproaches of quantum gravity.  In particular in this thesis we consider: the role that the changes ofmomentum variables play in a deformed relativistic kinematics; a novelconnection between the $\kappa$-Poincar\'e model and a curved momentum space; anew spacetime, which turns out to be noncommutative, making the interactionslocal; the possible time delay in the flight of photons as a consequence of adeformed kinematics, depending on whether observables are defined on acommutative or on a noncommutative spacetime; some computations in quantumfield theory with a simple ansatz for the modified Feynman rules correspondingto a particle process; the generalization of the geometrical approach for acurved spacetime.

Beyond special relativity and the notion of spacetime