  In this article, we deal with the following $p$-fractional
Schr\"{o}dinger-Kirchhoff equations with electromagnetic fields and the
Hardy-Littlewood-Sobolev nonlinearity: $$
M\left([u]_{s,A}^{p}\right)(-\Delta)_{p, A}^{s} u+V(x)|u|^{p-2}
u=\lambda\left(\int_{\mathbb{R}^{N}} \frac{|u|^{p_{\mu, s}^{*}}}{|x-y|^{\mu}}
\mathrm{d}y\right)|u|^{p_{\mu, s}^{*}-2} u+k|u|^{q-2}u,\ x \in
\mathbb{R}^{N},$$ where $0<s<1<p$, $ps < N$, $p<q<2p^{*}_{s,\mu}$, $0<\mu<N$,
$\lambda$ and $k$ are some positive parameters,
$p^{*}_{s,\mu}=\frac{pN-p\frac{\mu}{2}}{N-ps}$ is the critical exponent with
respect to the Hardy-Littlewood-Sobolev inequality, and functions $V$, $M$
satisfy the suitable conditions. By proving the compactness results with the
help of the fractional version of concentration compactness principle, we
establish the existence of nontrivial solutions to this problem.
