Abstract: What does a stochastic path look like when it is forced to cross an unusually high barrier?  We survey infinite- and finite-horizon first-passage probabilities and show how conditioning on the rare event shapes the Brownian bridge into a “flat-then-spike” profile.  We then ask the question what happens when the path is no longer continuous and turn to Lévy processes with light, semi-heavy, and heavy tails. This leads to a taxonomy of path shapes for Lévy process conditioned to overshoot high levels within a fixed time window.