  In this work, we establish universal moduli of continuity for viscosity
solutions to fully nonlinear elliptic equations with oblique boundary
conditions, whose general model is given by $$ \left\{ \begin{array}{rcl}
F(D^2u,x) &=& f(x) \quad \mbox{in} \,\, \Omega\\ \beta(x) \cdot Du(x) +
\gamma(x) \, u(x)&=& g(x) \quad \mbox{on} \,\, \partial \Omega. \end{array}
\right. $$ Such regularity estimates are achieved by exploring the
integrability properties of $f$ based on different scenarios, making a
$\text{VMO}$ assumption on the coefficients of $F$, and by considering suitable
smoothness properties on the boundary data $\beta, \gamma$ and $g$.
Particularly, we derive sharp estimates for borderline cases where $f \in
L^n(\Omega)$ and $f\in p-\textrm{BMO}(\Omega)$. Additionally, for source terms
in $L^p(\Omega)$, for $p \in (n, \infty)$, we obtain sharp gradient estimates.
Finally, we also address Schauder-type estimates for convex/concave operators
and suitable H\"{o}lder data.
