  We study quantum mechanical tunneling using complex solutions of the
classical field equations. Simple visualization techniques allow us to unify
and generalize previous treatments, and straightforwardly show the connection
to the standard approach using Euclidean instanton solutions. We demonstrate
that the negative modes of solutions along various contours in the complex time
plane reveal which paths give the leading contribution to tunneling and which
do not, and we provide a criterion for identifying the negative modes. Central
to our approach is the solution of the background and perturbation equations
not only along a single path, but over an extended region of the complex time
plane. Our approach allows for a fully continuous and coherent treatment of
classical evolution interspersed by quantum tunneling events, and is applicable
in situations where singularities are present and also where Euclidean
solutions might not exist.
