  Higher-spin diffeomorphisms are to higher-order differential operators what
diffeomorphisms are to vector fields. Their rigorous definition is a
challenging mathematical problem which might predate a better understanding of
higher-spin symmetries and interactions. Several yes-go and no-go results on
higher-spin diffeomorphisms are collected from the mathematical literature in
order to propose a generalisation of the algebra of differential operators on
which higher-spin diffeomorphisms are well-defined.
