  In this thesis we consider primarily the dynamics of quantum systems
subjected to continuous observation. In the Schr\"{o}dinger picture the
evolution of a continuously monitored quantum system, referred to as a `quantum
trajectory', may be described by a stochastic equation for the state vector. We
present a method of deriving explicit evolution operators for linear quantum
trajectories, and apply this to a number of physical examples of varying
mathematical complexity.
  In the Heisenberg picture evolution resulting from continuous observation may
be described by quantum Langevin equations. We use this method to examine the
noise spectrum that results from a continuous observation of the position of a
moving mirror, and examine the possibility of detecting the noise resulting
from the quantum back-action of the measurement.
  In addition to the work on continuous measurement theory, we also consider
the problem of reconstructing the state of a quantum system from a set of
measurements. We present a scheme for determining the state of a single cavity
mode from the photon statistics measured both before and after an interaction
with one or two two-level atoms.
