  In this report the exact rotating charged black hole solution to the
Einstein--nonlinear electrodynamics theory with a cosmological constant is
presented. This black hole is equipped with mass, rotation parameter, electric
and magnetic charges, cosmological constant $\Lambda$, and three parameters due
to the nonlinear electrodynamics: $\beta$ is associated to the potential
vectors $A_\mu$ and ${}^{\star}P_\mu$, and two constants, $F_0$ and $G_0$, due
to the presence of the invariants $F$ and $G$ in the Lagrangian
$L(F(\,x^{\mu}),G(\,x^{\mu}))$. This solution is of Petrov type D,
characterized by the Weyl tensor eigenvalue $\Psi_2$, the traceless Ricci
tensor eigenvalue $S=2\Phi_{(11)}$, and the scalar curvature $R$; it allows for
event horizons, exhibits a ring singularity and fulfils the energy conditions.
Its Maxwell limit is the de Sitter-Anti--de Sitter--Kerr--Newman black hole
solution.
