Two methods are presented for determining advanced combinatorial identities. The first is based on extending the original identity so that it can be expressed in terms of hypergeometric functions whereupon tabulated values of the functions can be used to reduce the identity to a simpler form. The second is a computer method based on Koepf's version of the Wilf-Zeilberger approach that has been implemented in a suite of intrinsic routines in Maple. As a consequence, some new identities are presented.