The paper proposes a new mechanism for the generation of dark matter, called "thermal freeze-in," which involves a Feebly Interacting Massive Particle (FIMP) that interacts so weakly with the thermal bath that it never reaches thermal equilibrium. Unlike the conventional "thermal freeze-out" mechanism, the relic abundance of FIMP dark matter is determined by a combination of initial thermal distributions, particle masses, and couplings that can be measured in the laboratory or astrophysically. The freeze-in yield is dominated by low temperatures near the FIMP mass and is independent of unknown UV physics, such as the reheat temperature after inflation. The paper discusses various models that implement the freeze-in mechanism, including moduli and modulinos of string theory compactifications that receive mass from weak-scale supersymmetry breaking, models with Dirac neutrino masses, and models involving GUT-scale-suppressed interactions. Experimental signals of freeze-in and FIMPs can be significant, including the production of new metastable colored or charged particles at the LHC and the alteration of big bang nucleosynthesis. The paper also presents "abundance phase diagrams" that illustrate the regions of mass and coupling where each mechanism dominates the production of the relic abundance.The paper proposes a new mechanism for the generation of dark matter, called "thermal freeze-in," which involves a Feebly Interacting Massive Particle (FIMP) that interacts so weakly with the thermal bath that it never reaches thermal equilibrium. Unlike the conventional "thermal freeze-out" mechanism, the relic abundance of FIMP dark matter is determined by a combination of initial thermal distributions, particle masses, and couplings that can be measured in the laboratory or astrophysically. The freeze-in yield is dominated by low temperatures near the FIMP mass and is independent of unknown UV physics, such as the reheat temperature after inflation. The paper discusses various models that implement the freeze-in mechanism, including moduli and modulinos of string theory compactifications that receive mass from weak-scale supersymmetry breaking, models with Dirac neutrino masses, and models involving GUT-scale-suppressed interactions. Experimental signals of freeze-in and FIMPs can be significant, including the production of new metastable colored or charged particles at the LHC and the alteration of big bang nucleosynthesis. The paper also presents "abundance phase diagrams" that illustrate the regions of mass and coupling where each mechanism dominates the production of the relic abundance.