  The framework of locally covariant quantum field theory, an axiomatic
approach to quantum field theory in curved spacetime, is reviewed. As a
specific focus, the connection between spin and statistics is examined in this
context. A new approach is given, which allows for a more operational
description of theories with spin and for the derivation of a more general
version of the spin-statistics connection in curved spacetimes than previously
available. This part of the text is based on arXiv:1503.05797 and a forthcoming
publication; the emphasis here is on the fundamental ideas and motivation.
