We examine the quantum field theory of scalar field in non-Minkowski spacetimes. We first develop a model of a uniformly accelerating particle detector and demonstrate that it will detect a thermal spectrum of particles when the field is in an "empty" state (according to inertial observers). We then develop a formalism for relating field theories in different coordinate systems (Bogolubov transformations),and apply it to compare comoving observers in Minkowski and Rindler spacetimes. Rindler observers are found to see a hot bath of particles in the Minkowski vacuum, which confirms the particle detector result. The temperature is found to be proportional to the proper acceleration of comoving Rindler observers. This is generalized to 2D black hole spacetimes, where the Minkowski frame is related to Kruskal coordinates and the Rindler frame is related to conventional (t; r) coordinates. We determine that when the field is in the Kruskal (Hartle-Hawking) vacuum, conventional observers will conclude that the black hole acts as a blackbody of temperature ยท=2pi*kB (kB is Boltzmann's constant). We examine this result in the context of static particle detectors and thermal Green's functions derived from the 4D Euclidean continuation of the Schwarzschild manifold. Finally, we givea semi-qualitative 2D account of the emission of scalar particles from a ball of matter collapsing into a black hole (the Hawking effect).