  This paper is devoted to the study of the following fractional Choquard
equation $$ \varepsilon^{2s}(-\Delta)^{s} u + V(x)u =
\varepsilon^{\mu-N}\left(\frac{1}{|x|^{\mu}}*F(u)\right)f(u) \mbox{ in }
\mathbb{R}^{N}, $$ where $\varepsilon>0$ is a parameter, $s\in (0, 1)$, $N>2s$,
$(-\Delta)^{s}$ is the fractional Laplacian, $V$ is a positive continuous
potential with local minimum, $0<\mu<2s$, and $f$ is a superlinear continuous
function with subcritical growth. By using the penalization method and the
Ljusternik-Schnirelmann theory, we investigate the multiplicity and
concentration of positive solutions for the above problem.
