  In this paper we study various scribability problems for polytopes. We begin
with the classical $k$-scribability problem proposed by Steiner and generalized
by Schulte, which asks about the existence of $d$-polytopes that cannot be
realized with all $k$-faces tangent to a sphere. We answer this problem for
stacked and cyclic polytopes for all values of $d$ and $k$. We then continue
with the weak scribability problem proposed by Gr\"unbaum and Shephard, for
which we complete the work of Schulte by presenting non weakly circumscribable
$3$-polytopes. Finally, we propose new $(i,j)$-scribability problems, in a
strong and a weak version, which generalize the classical ones. They ask about
the existence of $d$-polytopes that can not be realized with all their
$i$-faces "avoiding" the sphere and all their $j$-faces "cutting" the sphere.
We provide such examples for all the cases where $j-i \le d-3$.
