  Twisted bilayer graphene has a rich phase diagram, including
superconductivity. Recently, an unexpected discovery has been the observation
of superconductivity in non-twisted graphene bilayers and trilayers. In this
Perspective, we give an overview of the search for uncommon phases in
non-twisted graphene systems. We first contextualize these recent results
within earlier work in the field, before examining the new experimental
findings. Finally, we analyse the numerous theoretical models that study the
underlying physical processes in these systems
