  Classical results and recent developments on the theoretical description of
elementary particles with "continuous" spin are reviewed. At free level, these
fields are described by unitary irreducible representations of the isometry
group (either Poincar\'e or anti de Sitter group) with an infinite number of
physical degrees of freedom per spacetime point. Their basic group-theoretical
and field-theoretical descriptions are reviewed in some details. We mention a
list of open issues which are crucial to address for assessing their physical
status and potential relevance.
