The study of deformations of singular foliations cannot be streamlined
as for regular foliations, due to the presence of singularities.
However, upon replacing the singular foliation by its corresponding Lie
infinity-algebroid, we can construct a DGLA whose Maurer-Cartan elements
control the deformations of the given singular foliation. It appears
that deforming the singular foliation amounts to deforming the
corresponding Lie infinity-structure. We use this approach to study the
deformations of several kinds of singular foliations. Work in
collaboration with Camille Laurent-Gengoux.