  We give an almost complete classification of non-big Ulrich vector bundles on
fourfolds. This allows to classify them in the case of Picard rank one
fourfolds, of Mukai fourfolds and in the case of Del Pezzo $n$-folds for $n \le
4$. We also classify Ulrich bundles with non-big determinant on Del Pezzo and
Mukai $n$-folds, $n \ge 2$.
