  We consider the six-vertex model on an $N \times N$ square lattice with the
domain wall boundary conditions. Boundary one-point correlation functions of
the model are expressed as determinants of $N\times N$ matrices, generalizing
the known result for the partition function. In the free fermion case the
explicit answers are obtained. The introduced correlation functions are closely
related to the problem of enumeration of alternating sign matrices and domino
tilings.
