  The aim of this paper is to study $ m $-isometric weighted shifts with
operator weights (both unilateral and bilateral). We obtain a characterization
of such shifts by polynomials with operator coefficients. The procedure of
construction of all $ m $-isometric weighted shifts with positive weights is
given. We answer the question when the weights of $ m $-isometric shifts are
commuting. The completion problem for $ m $-isometric weighted shifts with
operator weights is solved. We characterize $ m $-isometric bilateral shifts
the adjoints of which are also $ m $-isometric. Several relevant examples are
provided.
