  In this paper we consider the nonlinear Choquard equation $$ -\Delta u+V(x)u
=\left(\int_{\mathbb{R}^N}\frac{G(y,u)}{|x-y|^{\mu}}dy\right)g(x,u)\hspace{4.14mm}\mbox{in}\hspace{1.14mm}
\mathbb{R}^N, $$ where $0<\mu<N$, $N\geq3$, $g(x,u)$ is of critical growth due
to the Hardy--Littlewood--Sobolev inequality and
$G(x,u)=\displaystyle\int^u_0g(x,s)ds$. Firstly, by assuming that the potential
$V(x)$ might be sign-changing, we study the existence of Mountain-Pass solution
via a concentration-compactness principle for the Choquard equation. Secondly,
under the conditions introduced by Benci and Cerami \cite{BC1}, we also study
the existence of high energy solution by using a global compactness lemma for
the nonlocal Choquard equation.
