Appears in collection : General relativity: a celebration of the 100th anniversary

I will review several recent results concerning the study of wave equations in spacetimes which behaves near spatial infinity as the Anti-de-Sitter (AdS) space. In particular, my talk will cover the behavior of linear waves in asymptotically AdS black hole spacetimes and the conjectured instability of AdS for Dirichlet type boundary conditions as well as the decay properties of linear fields in AdS, including electromagnetic and Weyl fields, for absorbing boundary conditions obtained in joint work with Holzegel, Luk and Warnick. https://philippelefloch.files.wordpress.com/2015/11/2015-ihp-j-smulevici.pdf