Although dark matter has only been observed gravitationally, it would be an amazing coincidence if it did not interact at all with standard model particles. I will discuss a model of composite dark matter which appears as a bosonic neutral baryon of a new strongly coupled sector whose elementary constituents carry electroweak charges. This construction provides a mechanism to naturally reduce the strength of dark matter interactions with standard model particles. However such interactions exist and can allow direct detection, and collider experiments to put constraints on the model. In order to get predictions from this strongly-coupled model, lattice simulations are employed and give definite predictions for the cross-section of the dark matter candidate with standard nuclei in detectors for example. Lattice simulations are shown to be of outmost relevance for some dark matter models and they are increasingly important to obtain phenomenological predictions of experimental interest.