We review the list of non-degenerate invariant (super)symmetric bilinear
forms (briefly: NIS) on the following simple (relatives of) Lie
(super)algebras: (a) with symmetrizable Cartan matrix of any growth, (b) with
non-symmetrizable Cartan matrix of polynomial growth, (c) Lie (super)algebras
of vector fields with polynomial coefficients, (d) stringy a.k.a.
superconformal superalgebras, (e) queerifications of simple restricted Lie
algebras.
Over algebraically closed fields of positive characteristic, we establish
when the deform (i.e., the result of deformation) of the known
finite-dimensional simple Lie (super)algebra has a NIS. Amazingly, in most of
the cases considered, if the Lie (super)algebra has a NIS, its deform has a NIS
with the same Gram matrix after an identification of bases of the initial and
deformed algebras. We do not consider odd parameters of deformations.
Closely related with simple Lie (super)algebras with NIS is the notion of
doubly extended Lie (super)algebras of which affine Kac--Moody (super)algebras
are the most known examples.