  We give a survey of some old and new results about the stated skein
modules/algebras of 3-manifolds/surfaces. For generic quantum parameter, we
discuss the splitting homomorphism for the 3-manifold case, general structures
of the stated skein algebras of marked surfaces (or bordered punctured
surfaces) and their embeddings into quantum tori. For roots of 1 quantum
parameter, we discuss the Frobenius homomorphism (for both marked 3-manifolds
and marked surfaces), describe the center of the skein algebra of marked
surfaces, the dimension of the skein algebra over the center, and the
representation theory of the skein algebra. In particular, we show that the
skein algebra of non-closed marked surface at any root of 1 is a maximal order.
We give a full description of the Azumaya locus of the skein algebra of the
puncture torus and give partial results for closed surfaces.
