  In this review we discuss and compare the usage of simplified models and
Effective Field Theory (EFT) approaches in dark matter searches. We provide a
state of the art description on the subject of EFTs and simplified models,
especially in the context of collider searches for dark matter, but also with
implications for direct and indirect detection searches, with the aim of
constituting a common language for future comparisons between different
strategies. The material is presented in a form that is as self-contained as
possible, so that it may serve as an introductory review for the newcomer as
well as a reference guide for the practitioner.
