  The notion of topology in physical systems is associated with the existence
of a nonlocal ordering that is insensitive to a large class of perturbations.
This brings robustness to the behaviour of the system and can serve as a ground
for developing new fault-tolerant applications. We discuss how to design and
study a large variety of topology-related phenomena for phonon-like collective
modes in arrays of ultracold polarized dipolar particles. These modes are
coherently propagating vibrational excitations, corresponding to oscillations
of particles around their equilibrium positions, which exist in the regime
where long-range interactions dominate over single-particle motion. We
demonstrate that such systems offer a distinct and versatile tool to
investigate a wide range of topological effects in a single experimental setup
with a chosen underlying crystal structure by simply controlling the anisotropy
of the interactions via the orientation of the external polarizing field. Our
results show that arrays of dipolar particles provide a promising unifying
platform to investigate topological phenomena with phononic modes.
