  Certain approaches to quantum gravity and classical modified gravity theories
result in effective field equations in which the original source is substituted
by an effective one. In these cases, the occurrence of regular spacetime
configurations may be related to the regularity of the effective source,
regardless of the specific mechanism behind the regularization. In this
chapter, we make an introduction to the effective source formalism applied to
higher-derivative gravity. The results presented here, however, can be easily
transposed to other frameworks that use similar sources. The generality
obtained is also because we consider a general higher-derivative gravity model
instead of restricting the analysis to some specific theories. In the first
part, we discuss the model in the Newtonian limit, which offers a natural
context for introducing effective sources. We show how the regularity
properties of the effective sources depend on the behavior of the action's form
factor in the ultraviolet regime, which leads to results valid for large
families of models (or for families of modified delta sources). Subsequently,
we use the general results on the effective sources to construct regular black
hole metrics. One of our concerns is the higher-order regularity of the
solutions, i.e., the possibility that not only the invariants built with
curvature tensors but also the ones with covariant derivatives are regular. In
this regard, we present some theorems relating the regularity of sets of
curvature-derivative invariants with the regularity properties of the effective
sources.
