  This article serves as an introduction to the linear aspects of the recent
submission by Krieger, Miao, and the author, see arXiv:2009.08843. It also
surveys some of the results obtained on the decay of linear waves on various
backgrounds or in the presence of a potential over the past 15 years.
Particular emphasis is placed on the role of 0 energy. The techniques are based
on spectral and scattering theory. Note that this is not a systematic review,
as this would require a book.
