Basic definitions and notation.- Survey of continued fraction methods of solving moment problems and related topics.- Modifications of continued fractions, a survey.- Convergence acceleration for continued fractions K(an/1) with lim an=0.- Truncation error analysis for continued fractions K(an/1) where .- A method for convergence acceleration of continued fractions K(an/1).- Some periodic sequences of circular convergence regions.- Some useful formulas involving tails of continued fractions.- Uniform twin-convergence regions for continued fractions K(an/1).- Digital filters and continued fractions.- ?-Fraction expansions of analytic functions.- On the structure of the two-point padé table.- A class of element and value regions for continued fractions.- Parameterizations and factorizations of element regions for continued fractions K(an/1).- On a certain transformation of continued fractions.