  On a Riemannian manifold of dimension $2 \leq d \leq 6$, with or without
boundary, and whether bounded or unbounded, we consider a semilinear wave (or
Klein-Gordon) equation with a subcritical nonlinearity, either defocusing or
focusing. We establish local controllability around a partially analytic
solution, under the geometric control condition. Specifically, some blow-up
solutions can be controlled. In the case of a Klein-Gordon equation on a
non-trapping exterior domain, we prove the null-controllability of scattering
solutions. The proof is based on local energy decay and global-in-time
Strichartz estimates. Some corollaries are given, including the
null-controllability of a solution starting near the ground state in certain
focusing cases, and exact controllability in certain defocusing cases.
