  We study the construction of probability densities for time-of-arrival in
quantum mechanics. Our treatment is based upon the facts that (i) time appears
in quantum theory as an external parameter to the system, and (ii) propositions
about the time-of-arrival appear naturally when one considers histories. The
definition of time-of-arrival probabilities is straightforward in stochastic
processes. The difficulties that arise in quantum theory are due to the fact
that the time parameter of Schr\"odinger's equation does not naturally define a
probability density at the continuum limit, but also because the procedure one
follows is sensitive on the interpretation of the reduction procedure. We
consider the issue in Copenhagen quantum mechanics and in history-based schemes
like consistent histories. The benefit of the latter is that it allows a proper
passage to the continuous limit--there are however problems related to the
quantum Zeno effect and decoherence. We finally employ the histories-based
description to construct Positive-Operator-Valued-Measures (POVMs) for the
time-of-arrival, which are valid for a general Hamiltonian. These POVMs
typically depend on the resolution of the measurement device; for a free
particle, however, this dependence cancels in the physically relevant regime
and the POVM coincides with that of Kijowski.
