Active chiral nematics are composed of a large number of self-locomoting constituents with inherently incorporated chirality, which are capable of converting the energy into motion, thereby driving the system out of thermodynamical equilibrium. In this Master's thesis we explore the effect of chiralty in active nematics in 2 or 3 dimensions and different confined geometries using numerical simulations. The simulations are based on the Beris-Edwards model of nematodynamics adapted for activity, which is solved using the hybrid lattice-Boltzmann method. In the model, especially, we explore the role of the additional chiral term in the elastic energy and the active term in the stress tensor. The stationary active states were explored in different systems, including in a free cell with periodic boundary conditions in a quasi-2D system and near an undulated surface. We show that chirality affects the active state as it imposes twist deformations, which are not a source of active stress. Thereby, the average velocity in the system is effectively reduced and active turbulence is less pronounced which is most noticable in the case of moderate activity. Typically, the disclination lines in 3D chiral systems no longer have the local structure of a $+1/2$ defect, but acquire local components of twist disclination, which slows their dynamics. In the case of quasi-2D systems we observe the formation of active skyrmion lattices with characteristic velocity profiles in addition to the nematic regime and active turbulence. In restricted geometries, we observe stable defects at moderate activity, while active turbulent regime at high activities is observed regardless of the boundary conditions. The demonstrated work is a contribution towards understanding active materials, especially active nematic fluids, which are today a world broad and rapidly growing field of research.