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We perform a detailed study of the geodesic equations in the spacetime of thestatic and rotating charged black hole corresponding to the Kerr-Newman-(A)dSspacetime. We derive the equations of motion for test particles and light raysand present their solutions in terms of the Weierstrass $\wp$, $\zeta$ and$\sigma$ functions as well as the Kleinian $\sigma$ function. With the help ofparametric diagrams and effective potentials we analyze the geodesic motion andclassify the possible orbit types. This spacetime is also a solution of $f(R)$gravity with a constant curvature scalar.

Detailed study of geodesics in the Kerr-Newman-(A)dS spactime and the rotating charged black hole spacetime in $f(R)$ gravity