  This is a survey concerning the relationship between Lie Groupoids (and their
morphisms) and singular foliations in the sense of Sussmann-Stefan (considered
from a purely geometrical point of view). We focus on the interaction between
the algebraic and differentiable structures underlying Lie groupoids, and
between groups and graphs of equivalence relations, regarded as two basic
degeneracies for groupoids. Historical remarks, motivations and examples are
developed in five appendices.
