In Bell's inequalities, how is realism violated, and how can one preserve locality? I have heard the violation of Bell's inequalities asserts either realism or locality needs to be abandoned. I understand the notion of locality being violated but can someone explain how realism is violated assuming locality is preserved and how one can even preserve locality? Thanks 
 A: Realism, in the context of the EPR paradox, is the assumption that properties have a definite state even when not measured; just like how Locality means that information is locally bound, ie, cannot travel faster than light.
Note: More concretely, we refer to this definition of 'reality' as Counterfactual Definiteness.
If we assume the act of measurement itself creates a definite state, then we can sacrifice realism and keep locality. However, since it is easier to argue for a loss of locality, most interpretations go that route.
Some interpretations do drop this assumption instead, see https://en.wikipedia.org/wiki/Counterfactual_definiteness#Examples_of_interpretations_rejecting_counterfactual_definiteness
Note that the EPR paradox also makes two other assumptions:
1: Quantum Mechanics is 'complete'; it accurately describes reality without hidden variables. (explicitly stated)
2: the universe is fair, it does not hide results. (Implicit assumption)
Note that Einstein's argument was in favour of these local hidden variables (thus against 'completeness'), which are disproven by the Bell Tests. (The bell-tests do not preclude nonlocal hidden variables, but those would still violate local realism)
Similarly, if we assume that the universe is hiding results that do not match the results of the Bell Tests, it is easy to resolve the paradox; however, since this assumption is at the basis of all science, it would invalidate any other work done.
Additional note: there are some interpretations that do away with the paradox altogether, by positing that local realism is ill-defined. One such example is the relational interpretation (https://en.m.wikipedia.org/wiki/Relational_quantum_mechanics), which posits that, when you look from an individual observer, information about the far end of a system only reaches the observer after a light-speed delay, meaning that neither locality nor realism have to be violated, so long as we make them observer bound.
