  We investigate global H\"older gradient estimates for solutions to the
Monge-Amp\`ere equation $$\mathrm{det}\;D^2 u=f\quad\mathrm{in}\;\Omega,$$
where the right-hand side $f$ is bounded away from $0$ and $\infty$. We
consider two main situations when a) the domain $\Omega$ is uniformly convex
and b) $\Omega$ is flat.
