  Quantum field theory on curved spacetimes lacks an obvious distinguished
vacuum state. We review a recent no-go theorem that establishes the
impossibility of finding a preferred state in each globally hyperbolic
spacetime, subject to certain natural conditions. The result applies in
particular to the free scalar field, but the proof is model-independent and
therefore of wider applicability. In addition, we critically examine the
recently proposed "SJ states", that are determined by the spacetime geometry
alone, but which fail to be Hadamard in general. We describe a modified
construction that can yield an infinite family of Hadamard states, and also
explain recent results that motivate the Hadamard condition without direct
reference to ultra-high energies or ultra-short distance structure.
