Quantum Computing

The classic EPR-esque thought experiments is an illustration of this. Particle A and particle B take on values of either +1 or -1 at random, but are guaranteed to be opposite. They are sent to two different labs very far apart so Alice gets particle A and Bob gets particle B. Alice measures her particle and finds that, by happenstance, she gets +1, and now this must mean Bob's is influenced to become -1. You cannot use this to signal for two reasons. First, the values both of their particles take on is random and so the nonlocal influence is random, so no information can be encoded in the +1 vs -1. Second, Bob cannot even notice if Alice does this, because if he tries to measure his particle, he will just be the one who measures a random value that then fixes Alice's particle.

This is nonlocal in Einstein's definition of locality, but since you cannot signal with it, it technically does not violate special relativity, so many contemporary physicists define locality in terms of being able to signal, so they would label this as local, even though there is literally instantaneous influence between the particles.