  We investigate the integrable structure of spin chain models with centrally
extended su(2|2) and psu(2,2|4) symmetry. These chains have their origin in the
planar AdS/CFT correspondence, but they also contain the one-dimensional
Hubbard model as a special case. We begin with an overview of the
representation theory of centrally extended su(2|2). These results are applied
in the construction and investigation of an interesting S-matrix with su(2|2)
symmetry. In particular, they enable a remarkably simple proof of the
Yang-Baxter relation. We also show the equivalence of the S-matrix to Shastry's
R-matrix and thus uncover a hidden supersymmetry in the integrable structure of
the Hubbard model. We then construct eigenvalues of the corresponding transfer
matrix in order to formulate an analytic Bethe ansatz. Finally, the form of
transfer matrix eigenvalues for models with psu(2,2|4) symmetry is sketched.
