  We overview classifications of simple infinite-dimensional complex
$\mathbb{Z}$-graded Lie (super)algebras of polynomial growth, and their
deformations. A subset of such Lie (super)algebras consist of vectorial Lie
(super)algebras whose elements are vector fields with polynomial, or formal
power series, or divided power coefficients. A given vectorial Lie
(super)algebra with a (Weisfeiler) filtration corresponding to a maximal
subalgebra of finite codimension is called W-filtered; the associated graded
algebra is called W-graded. Here, we correct several published results: (1)
prove our old claim "the superization of \'E. Cartan's problem (classify
primitive Lie algebras) is wild", (2) solve a tame problem: classify simple
W-graded and W-filtered vectorial Lie superalgebras, (3) describe the
supervariety of deformation parameters for the serial W-graded simple vectorial
superalgebras, (4) conjecture that the exceptional simple vectorial
superalgebras are rigid. We conjecture usefulness of our method in
classification of simple infinite-dimensional vectorial Lie (super)algebras
over fields of positive characteristic.
