  A detailed real time description of quantum tunneling in the semiclassical
limit is given, using complex classical trajectories. This picture connects
naturally with the ideas of post-selection and weak measurement introduced by
Aharonov and collaborators. I show that one can precisely identify the {\it
complex} classical trajectory which a post-selected tunneling particle has
followed, and which dominates the path integral in the limit as Planck's
constant $\hbar$ tends to zero. Detailed analytical calculations are presented
for tunneling in cubic and quartic potentials. For a long post-selected
tunneling time, the imaginary part of the tunneling coordinate is found to
achieve very large values just before the particle tunnels. I discuss how the
real and imaginary parts of the particle's coordinate may, in principle, be
independently measured using weak measurements. It would be very interesting to
observe this effect, which would demonstrate the essential role of complex
numbers in our closest possible classical description of reality. Extensions to
quantum field theory and general relativity are briefly discussed.
