Are there decision problems outside of NP?
The nondeterministic time hierarchy theorem shows that, e.g., $\mathrm{NP}\subsetneq\mathrm{NEXP}$, so any $\mathrm{NEXP}$-complete problem is $\mathrm{NP}$-hard but not in&nbsp;$\mathrm{NP}$.  For a more extreme example, the halting problem is $\mathrm{NP}$-hard but not in&nbsp;$\mathrm{NP}$.