  It was recently shown that Aharonov-Bohm (AB) cages exist for quantum walks
(QW) on certain tilings -- such as the diamond chain or the dice (or
$\mathcal{T}_3$) lattice -- for a proper choice of coins. In this article, we
probe the robustness of these AB cages to various perturbations. When the cages
are destroyed, we analyze the leakage mechanism and characterize the resulting
dynamics. Quenched disorder typically breaks the cages and leads to an
exponential decay of the wavefunction similar to Anderson localization.
Dynamical disorder or repeated measurements destroy phase coherence and turn
the QW into a classical random walk with diffusive behavior. Combining static
and dynamical disorder in a specific way leads to subdiffusion with an
anomalous exponent controlled by the quenched disorder distribution.
Introducing interaction to a second walker can also break the cages and restore
a ballistic motion for a "molecular" bound-state.
