  We give new interpretations of the $\nu$-Tamari lattice of Pr\'eville-Ratelle
and Viennot. First, we describe it as a rotation lattice of $\nu$-trees, which
uncovers the relation with known combinatorial objects such as tree-like
tableaux and north-east fillings. Then, using a formulation in terms of bracket
vectors of $\nu$-trees and componentwise order, we provide a simple description
of the lattice property. We also show that the $\nu$-Tamari lattice is
isomorphic to the increasing-flip poset of a suitably chosen subword complex,
and settle a special case of Rubey's lattice conjecture concerning the poset of
pipe dreams defined by chute moves. Finally, this point of view generalizes to
multi $\nu$-Tamari complexes, and gives (conjectural) insight on their
geometric realizability via polytopal subdivisions of multiassociahedra.
