Abstract: In this talk we present some recent results on the occurrence of regular solutions in local and nonlocal higher-derivative gravity models. In the first part, we show that even though fourth-order gravity still has curvature singularities, any local model with at least six derivatives in both spin-2 and spin-0 sectors has a regular Newtonian limit, without curvature singularities, when coupled to a pointlike source. Also, we discuss the general conditions for the regularity of the higher-order curvature invariants, in both local and nonlocal models. In the second part of the talk we comment on the effects that the leading logarithmic quantum corrections can have to these solutions, in both UV and IR limits. Finally, in the third part we discuss the collapse of a small mass, considered as a spherical superposition of gyratons, in a general polynomial model and verify the regularity and the existence of the mass gap for the formation of mini black holes.