Charged rotating black holes with (anti-)de Sitter asymptotics due to a non-zero cosmological constant can be modeled by the most general stationary black-hole solution within the framework of classical 4D general relativity---the Kerr-Newman-(anti-)de Sitter space-time. First, we briefly review some of the space-time's general properties and then we talk about the possible extremal configurations.
Finally, using Lagrangian formalism we discuss selected trajectories of charged test particles in the space-time, focusing on the equatorial plane and the axis.