  We investigate Hawking radiation from black holes in (d+1)-dimensional
anti-de Sitter space. We focus on s-waves, make use of the geometrical optics
approximation, and follow three approaches to analyze the radiation. First, we
compute a Bogoliubov transformation between Kruskal and asymptotic coordinates
and compare the different vacua. Second, following a method due to Kraus,
Parikh, and Wilczek, we view Hawking radiation as a tunneling process across
the horizon and compute the tunneling probablility. This approach uses an
anti-de Sitter version of a metric originally introduced by Painleve for
Schwarzschild black holes. From the tunneling probability one also finds a
leading correction to the semi-classical emission rate arising from the
backreaction to the background geometry. Finally, we consider a spherically
symmetric collapse geometry and the Bogoliubov transformation between the
initial vacuum state and the vacuum of an asymptotic observer.
