In this paper, the role of three-nucleon forces in ab initio calculations of nuclear systems is investigated. The difference between genuine and induced many-nucleon forces is emphasized. Induced forces arise in the process of solving the nuclear many-body problem as technical intermediaries toward calculationally converged results. Genuine forces make up the Hamiltonian. They represent the chosen underlying dynamics. The hierarchy of contributions arising from genuine two-, three- and many-nucleon forces is discussed. Signals for the need of the inclusion of genuine three-nucleon forces are studied in nuclear systems, technically best under control, especially in three-nucleon and four-nucleon systems. Genuine three-nucleon forces are important for details in the description of some observables. Their contributions to observables are small on the scale set by two-nucleon forces.