The holographic model of V-QCD is used to analyze the physics of QCD in the Veneziano large-N limit. An unprecedented analysis of the CP-odd physics is performed going beyond the level of effective field theories. The structure of holographic saddle points at finite θ is determined, as well as its interplay with chiral symmetry breaking. Many observables (vacuum energy and higher-order susceptibilities, singlet and nonsinglet masses and mixings) are computed as functions of θ and the quark mass m. Wherever applicable the results are compared to those of chiral Lagrangians, finding agreement. In particular, we recover the Witten-Veneziano formula in the small x→0 limit, we compute the θ dependence of the pion mass, and we derive the hyperscaling relation for the topological susceptibility in the conformal window in terms of the quark mass.