Different interpretations of QM suggest different things. There's no wave/particle duality in Bohmian mechanics: there's literally a wave, and literally a particle, and the particle is guided by the wave.
And the many-worlds interpretation does yet a third thing. They all make the same predictions of measurements though, which means it's rather a matter of philosophy and/or practicality which one you subscribe to.
"The universe seems to like talking to itself faster than the speed of light,” said Steinberg. “I could understand a universe where nothing can go faster than light, but a universe where the internal workings operate faster than light, and yet we’re forbidden from ever making use of that at the macroscopic level — it’s very hard to understand.”
This can only lead to one conclusion: the Universe is a computer program. We can observe some of the side effects of the underlying computer, but we cannot use it from inside the simulation.
Local hidden variables have been ruled out, notably by experiments with Bell's inequality.
This means that quantum effects cannot be caused by some unseen property of the objects involved (e.g. if particles had some extra 'charge' we didn't know about).
The effects could be caused by some unseen "non-local" property, e.g. some property of space itself which propagates faster than light. A nice example is to model spacetime as a network (e.g. http://www.wolframscience.com/nks/p475--space-as-a-network ) with information/causality propagating along edges in the network. If most of the edges are short, and form a 3D lattice, we'd get the universe we're familiar with. We can then model quantum phenomena, like entanglement, by introducing some long edges, connecting regions of the network which would otherwise be far apart (the entangled particles).
Since there are so many possible non-local theories, with no way to distinguish between them, Physicists tend to prefer quantum descriptions of local, observable properties, since that seems like less of a leap of faith.
And if you assume standard probability theory holds. If you allow for so called Exotic Probability, then local hidden variable theories are not ruled out. See [1] for a list of relevant literature.
Relational quantum mechanics does something else: https://en.wikipedia.org/wiki/Relational_quantum_mechanics
And the many-worlds interpretation does yet a third thing. They all make the same predictions of measurements though, which means it's rather a matter of philosophy and/or practicality which one you subscribe to.