Well, in the case of quantum entanglement, we don't really know how it works (kinda like gravity), but we can pretty easily (with varying definitions of "easily") reproduce the entanglement effect in a laboratory. As a matter of fact, it is the basis of the entire field of quantum computing, which I believe that IBM's Watson Labs has an early prototype of a quantum "CPU". Likely, the NSA has something too.
So, Cliffs:
- we don't know how it works
- we see the effect in experiments
- it works well enough that we already have applications of its power in proof-of-concept hardware
BB-related: Look at this perfect fucking bicep!