  In this paper, we introduce the so-called elliptic Askey-Wilson polynomials
which are homogeneous polynomials in two special theta functions. With regard
to the significance of polynomials of such kind, we establish some general
elliptic interpolation formulas by the methods of matrix inversions and of
polynomial representations. Furthermore, we find that the basis of elliptic
interpolation space due to Schlosser can be uniquely characterized via the
elliptic Askey-Wilson polynomials. As applications of these elliptic
interpolation formulas, we establish some new elliptic function identities,
including an extension of Weierstrass' theta identity, a generalized elliptic
Karlsson-Minton type identity, and an elliptic analogue of Gasper's summation
formula for very-well-poised ${}_{6+2m}\phi_{5+2m}$ series.
