  Unruh-DeWitt particle detector models are studied in a variety of
time-dependent and time-independent settings. We work within the framework of
first-order perturbation theory and couple the detector to a massless scalar
field. The necessity of switching on (off) the detector smoothly is emphasised
throughout, and the transition rate is found by taking the sharp-switching
limit of the regulator-free and finite response function. The detector is
analysed on a variety of spacetimes: $d$-dimensional Minkowski, the
Ba\~nados-Teitelboim-Zanelli (BTZ) black hole, the two-dimensional Minkowski
half-plane, two-dimensional Minkowski with a receding mirror, and the two- and
four-dimensional Schwarzschild black holes. In $d$-dimensional Minkowski
spacetime, the transition rate is found to be finite up to dimension five. In
dimension six, the transition rate diverges unless the detector is on a
trajectory of constant proper acceleration, and the implications of this
divergence to the global embedding spacetime (GEMS) methods are studied. In
three-dimensional curved spacetime, the transition rate for the scalar field in
an arbitrary Hadamard state is found to be finite and regulator-free. Then on
the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole spacetime, we analyse the
detector coupled to the field in the Hartle-Hawking vacua, under both
transparent and reflective boundary conditions at infinity. Results are
presented for the co-rotating detector, which responds thermally, and for the
radially-infalling detector. In four-dimensional Schwarzschild spacetime, we
proceed numerically, and the Hartle-Hawking, Boulware and Unruh vacua rates are
compared. Results are presented for the case of the static detectors, which
respond thermally, and also for the case of co-rotating detectors.
