I shall first recall the definition of the space of arcs of an algebraic variety V,
and the problem, proposed by J.Nash in the mid-sixties, concerning the irreducible components of the subscheme of those arcs centered in the singular locus of V. Then I will formulate some questions concerning these irreducible components, which stay open. Next, I will formulate questions on the graded algebra structure of the space of those arcs centered in a given point of V.
