Despite the success of describing physical phenomena on a microscopic level through the known electromagnetic, weak and strong forces, observations on the largest scales - accessible to us through astronomical and cosmological observations - yield a discordant picture when the apparent distribution of mass is used to compare these observations with the predictions made by gravity. This discrepancy is generally attributed to the presence of yet unknown “substrates” in the Universe, dark matter and dark energy. In this talk, I will review what brings us to adopt these notions. Focusing on dark matter, the various possibilities that can solve this problem of missing mass are discussed. As a solution might well be within the realm of particle physics, I will then discuss how to look for it in so-called direct detection experiments, i.e. laboratory probes that seek to register the ultra-rare interactions of galactic dark matter with ordinary matter. Here, I will show how recent advances in the theoretical understanding of these interactions allow us to significantly increase the sensitivity of existing searches, to increase their physics reach, and close with comments on where the field is heading.