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We consider inverse problems in space-time (M, g), a 4-dimensional Lorentzian manifold. For semilinear wave equations □gu+H(x,u)=f, where □g denotes the usual Laplace-Beltrami operator, we prove that the source-to-solution map L:f→u|V, where V is a neighborhood of a time-like geodesic μ, determines the topological, differentiable structure and the conformal class of the metric of the space-time in the maximal set, where waves can propagate from μ and return back. Moreover, on a given space-time (M, g), the source-to-solution map determines some coefficients of the Taylor expansion of H in u. [ABSTRACT FROM AUTHOR]