Topological Susceptibility and QCD at Finite Theta Angle

In this chapter we provide a pedagogical introduction to the main theoretical aspects related to topology and $\theta$-dependence in Quantum Chromo-Dynamics (QCD), and to their phenomenological relevance in the Standard Model ($\eta^\prime$ physics, neutron electric dipole moment) and beyond (strong CP problem and the axion solution). We then provide an overview of the main analytic predictions for $\theta$-dependence obtained using several different approaches (chiral effective theories, large-$N$ arguments, semiclassical methods) and their regimes of validity, as well as a selection of the most recent numerical results about QCD topology obtained via Monte Carlo simulations of the lattice-discretized theory.