  The topic of measurement in relativistic quantum field theory is addressed in
this article. Some of the long standing problems of this subject are
highlighted, including the incompatibility of an instantaneous ``collapse of
the wavefunction'' with relativity of simultaneity, and the difficulty of
maintaining causality in the rules for measurement highlighted by ``impossible
measurement'' scenarios. Thereafter, the issue is considered from the
perspective of mathematical physics. To this end, quantum field theory is
described in a model-independent, operator algebraic setting, on generic
Lorentzian spacetime manifolds. The process of measurement is modelled by a
localized dynamical coupling between a quantum field called the ``system'', and
another quantum field, called the ``probe''. The result of the dynamical
coupling is a scattering map, whereby measurements carried out on the probe can
be interpreted as measurements of induced observables on the system. The
localization of the dynamical coupling allows it to derive causal relations for
the induced observables. It will be discussed how this approach leads to the
concept of selective or non-selective system state updates conditioned on the
result of probe measurements, which in turn allows it to obtain conditional
probabilities for consecutive probe measurements consistent with relativistic
causality and general covariance, without the need for a physical collapse of
the wavefunction. In particular, the problem of impossible measurements is
resolved. Finally, there is a brief discussion of accelerated detectors and
other related work.
