  We study the temporal aspects of quantum tunneling as manifested in
time-of-arrival experiments in which the detected particle tunnels through a
potential barrier. In particular, we present a general method for constructing
temporal probabilities in tunneling systems that (i) defines `classical' time
observables for quantum systems and (ii) applies to relativistic particles
interacting through quantum fields. We show that the relevant probabilities are
defined in terms of specific correlations functions of the quantum field
associated with tunneling particles. We construct a probability distribution
with respect to the time of particle detection that contains all information
about the temporal aspects of the tunneling process. In specific cases, this
probability distribution leads to the definition of a delay time that, for
parity-symmetric potentials, reduces to the phase time of Bohm and Wigner. We
apply our results to piecewise constant potentials, by deriving the appropriate
junction conditions on the points of discontinuity. For the double square
potential, in particular, we demonstrate the existence of (at least) two
physically relevant time parameters, the delay time and a decay rate that
describes the escape of particles trapped in the inter-barrier region. Finally,
we propose a resolution to the paradox of apparent superluminal velocities for
tunneling particles. We demonstrate that the idea of faster-than-light speeds
in tunneling follows from an inadmissible use of classical reasoning in the
description of quantum systems.
