  Increasing experimental evidence suggests the occurrence of filamentary
superconductivity in different (quasi) two-dimensional physical systems. In
this piece of work, we discuss the proposal that under certain circumstances,
this occurrence may be related to the competition with a phase characterized by
charge ordering in the form of charge-density waves. We provide a brief summary
of experimental evidence supporting our argument in two paradigmatic classes of
materials, namely transition metal dichalcogenides and cuprates
superconductors. We present a simple Ginzburg-Landau two-order-parameters model
as a starting point to address the study of such competition. We finally
discuss the outcomes of a more sophisticated model, already presented in the
literature and encoding the presence of impurities, and how it can be further
improved in order to really address the interplay between charge-density waves
and superconductivity and the possible occurrence of filamentary
superconductivity at the domain walls between different charge-ordered regions.
