  In this paper, we extend the notion of visibility relative to the Kobayashi
distance to domains in arbitrary complex manifolds. Visibility here refers to a
property resembling visibility in the sense of Eberlein--O'Neill for Riemannian
manifolds. Since it is difficult, in general, to determine whether domains are
Cauchy-complete with respect to the Kobayashi distance, we do not assume so
here. We provide many sufficient conditions for visibility. We establish a
Wolff--Denjoy-type theorem in a very general setting as an application. We also
explore some connections between visibility and Gromov hyperbolicity for
Kobayashi hyperbolic domains in the above setting.
