  This paper contains a survey of some ring-theoretic aspects of quantized
coordinate rings, with primary focus on the prime and primitive spectra. For
these algebras, the overall structure of the prime spectrum is governed by a
partition into strata determined by the action of a suitable group of
automorphisms of the algebra. We discuss this stratification in detail, as well
as its use in determining the primitive spectrum -- under suitable conditions,
the primitive ideals are precisely those prime ideals which are maximal within
their strata. The discussion then turns to the global structure of the
primitive spectra of quantized coordinate rings, and to the conjecture that
these spectra are topological quotients of the corresponding classical affine
varieties. We describe the solution to the conjecture for quantized coordinate
rings of full affine spaces and (somewhat more generally) affine toric
varieties. The final part of the paper is devoted to the quantized coordinate
ring of $n\times n$ matrices. We mention parallels between this algebra and the
classical coordinate ring, such as the primeness of quantum analogs of
determinantal ideals. Finally, we describe recent work which determined, for
the $3\times3$ case, all prime ideals invariant under the group of winding
automorphisms governing the stratification mentioned above.
