  Let $X$ be a L\'evy process with regularly varying L\'evy measure $\nu$. We
obtain sample-path large deviations for scaled processes $\bar X_n(t)
\triangleq X(nt)/n$ and obtain a similar result for random walks. Our results
yield detailed asymptotic estimates in scenarios where multiple big jumps in
the increment are required to make a rare event happen; we illustrate this
through detailed conditional limit theorems. In addition, we investigate
connections with the classical large deviations framework. In that setting, we
show that a weak large deviation principle (with logarithmic speed) holds, but
a full large deviation principle does not hold.
