  We show that if $X$ is an arc-like continuum, then for every point $x \in X$
there is a plane embedding of $X$ in which $x$ is an accessible point. This
answers a question posed by Nadler in 1972, which has become known as the
Nadler-Quinn problem in continuum theory. Towards this end, we develop the
theories of truncations and contour factorizations of interval maps. As a
corollary, we answer a question of Mayer from 1982 about inequivalent plane
embeddings of indecomposable arc-like continua.
