  We present mathematical, algorithmic, complexity, and implementation results
on the problem of computing the Jelonek set in 2D. This is the set in
$\mathbb{K}^2$ at which a polynomial map $f: \mathbb{K}^2 \to \mathbb{K}^2$ is
not proper. Our results make no assumptions on $f$ and are valid for
$\mathbb{K}= \mathbb{C}$ and $\mathbb{K} = \mathbb{R}$.
