This is an expanded version of the talk given at the conference
``Constructive Functions Tech-04''. We survey some recent results on canonical
representation and asymptotic behavior of polynomials orthogonal on the unit
circle with respect to an analytic weight. These results are obtained using the
steepest descent method based on the Riemann-Hilbert characterization of these
polynomials.Comment: 23 pages, 7 figures; To appear in Elect. Trans. Num. Anal.
Apparently, due to some missing .sty file, all integrals in version 2 were
gone. Version 3 is a mere correction of this proble
