  A norm one element $x$ of a Banach space is a Daugavet-point (respectively, a
$\Delta$-point) if every slice of the unit ball (respectively, every slice of
the unit ball containing $x$) contains an element, which is almost at distance
2 from $x$. We characterize Daugavet- and $\Delta$-points in Lipschitz-free
spaces. Furthermore, we construct a Lipschitz-free space with the
Radon--Nikod\'ym property and a Daugavet-point; this is the first known example
of such a Banach space.
