Dark matter particles can interact so weakly with the standard model fields that they may never have reached thermal equilibrium in the early universe. The relic density of such feebly interacting massive particles (FIMPs) is produced via the so-called freeze-in mechanism. This possibility can explain why we have not yet detected dark matter but is also appealing from a theoretical perspective since tiny couplings might be a consequence of heavy particles needed to solve different puzzles in particle physics. In this talk, I will overview the literature on FIMP phenomenology and present two testable FIMP models. The first model is a neutrino portal where three right-handed heavy neutrinos participate in the type-I seesaw mechanism while mediating interactions between the visible and dark sectors. If a sufficiently long early matter-dominated period occurred during the freeze-in process, FIMP self-annihilation becomes testable by indirect detection experiments. The second model is a Z' portal in which the SM fermions and a fermionic dark matter candidate are both charged under a new U(1) symmetry. Remarkably, the rich phenomenology of Z' bosons is currently constraining regions of the Z' parameter space in which the dark matter relic density is achieved via freeze-in.