Problems which are at least as hard as the hardest problems in NP.
problems are a subset of NP-hard problems.
Reduction using a turing machine (no idea how)
Indirect reduction from existing NP problems.
We can do this because we have already proved other problems in NP-hard reduce to these problems. As such we can just reduce this problems to a new problem we have, to establish the new problem is NP-hard.