Quantum fields in curved spacetime, a grand tour

I will review the development of quantum field theory in curved spacetime from its beginnings towards the new developments of current research. Emphasis will be put on the modern mathematical ond conceptual developments, among them operator algebraic and microlocal methods, the microlocal spectrum condition, quantum energy inequalities [on which there are also talks in the workshop program of Oct 3rd-4th by some of the leading specialists in the field] and generally convariant quantum field theory. I will review some of the recent results of these developments, and give an outlook on the lines of future research.