  Studies of dark matter lie at the interface of collider physics, astrophysics
and cosmology. Constraining models featuring dark matter candidates entails the
capability to provide accurate predictions for large sets of observables and
compare them to a wide spectrum of data. We present a framework which, starting
from a model lagrangian, allows one to consistently and systematically make
predictions, as well as to confront those predictions with a multitude of
experimental results. As an application, we consider a class of simplified dark
matter models where a scalar mediator couples only to the top quark and a
fermionic dark sector (i.e. the simplified top-philic dark matter model). We
study in detail the complementarity of relic density, direct/indirect detection
and collider searches in constraining the multi-dimensional model parameter
space, and efficiently identify regions where individual approaches to dark
matter detection provide the most stringent bounds. In the context of collider
studies of dark matter, we point out the complementarity of LHC searches in
probing different regions of the model parameter space with final states
involving top quarks, photons, jets and/or missing energy. Our study of dark
matter production at the LHC goes beyond the tree-level approximation and we
show examples of how higher-order corrections to dark matter production
processes can affect the interpretation of the experimental results.
