I will present sharp late-time pointwise asymptotics for semilinear wave equations with power nonlinearities on stationary, asymptotically flat spacetimes (including black hole exteriors). Under standard spectral and local energy decay hypotheses for perturbations of black-hole backgrounds, we show a clean dichotomy: cubic nonlinearities generate a nonlinear t^{-2} tail with an explicit coefficient, while for powers p \ge 4 the linear Price's law t^{-3} decay holds with a modified coefficient; in both regimes we identify the leading term throughout the forward causal domain via a blend of radiation-field methods and low-energy resolvent analysis. Joint work with Haoren Xiong.