In this talk, we investigate the regularity properties of solutions to a class of fully nonlinear nonlocal equations, both elliptic and degenerate. For the elliptic case, we establish optimal regularity results for equations with a right-hand side in $L^p$, where the regularity space depends on the value of $p$. In the degenerate case, we prove the existence of at least one viscosity solution belonging to the class $C_{loc}^{1, \alpha}$ for some constant $\alpha \in (0,1)$. Additionally, when the order of the operator is sufficiently close to 2, we derive regularity estimates in Hölder spaces for the gradient of any viscosity solution.