Higher-derivative corrections to the Einstein-Hilbert action are characteristic to many approaches to the quantization of gravity. The scales at which such higher-derivative terms might prove to be important varies widely between different scenarios, but one possibility is for terms quadratic in the curvature tensor to remain important for an appreciable range of scales before yet higher terms might come into play. The talk will consider spherically symmetric static solutions to gravity including such quadratic curvature terms in the action. The solution space includes Schwarzschild and non-Schwarzschild black holes, horizonless solutions coupling to distributional matter and also wormholes.