Interpolation of curves and surfaces is a fundamental problem in computer aided
geometric design (CAGD) and related fields of research. In this talk we shall
focus on interpolation of parametric curves (or data) by parametric polynomial
curves. In contrast to functional case, where a polynomial of degree n can, in
general, interpolate at most n+1 points, planar parametric polynomial curve of
degree n might interpolate as much as 2n points. This kind of interpolation is
known as ’geometric interpolation’. Some results and open problems related to
geometric interpolation will be presented and interpolation of special parametric
objects (such as circular arcs) will be briefly outlined.

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