  In this paper we use admissible covers to investigate the gonality of a
stable curve $C$ over $\mathbb{C}$. If $C$ is irreducible, we compare its
gonality to that of its normalization. If $C$ is reducible, we compare its
gonality to that of its irreducible components. In both cases we obtain lower
and upper bounds. Furthermore, we show that four admissible covers constructed
give rise to generically injective maps between Hurwitz schemes. We show that
the closures of the images of three of these maps are components of the
boundary of the target Hurwitz schemes, and the closure of the image of the
remaining map is a component of a certain codimension-1 subscheme of the
boundary of the target Hurwitz scheme.
