The Large and Small Magellanic Clouds (LMC and SMC), gas-rich dwarf companions of the Milky Way, are the nearest laboratories for detailed studies on the formation and survival of complex organic molecules (COMs) under metal poor conditions. To date, only methanol, methyl formate, and dimethyl ether have been detected in these galaxies -all three toward two hot cores in the N113 star-forming region in the LMC, the only extragalactic sources exhibiting complex hot core chemistry. We describe a small and diverse sample of the LMC and SMC sources associated with COMs or hot core chemistry, and compare the observations to theoretical model predictions. Theoretical models accounting for the physical conditions and metallicity of hot molecular cores in the Magellanic Clouds have been able to broadly account for the existing observations, but fail to reproduce the dimethyl ether abundance by more than an order of magnitude. We discuss future prospects for research in the field of complex chemistry in the low-metallicity environment. The detection of COMs in the Magellanic Clouds has important implications for astrobiology. The metallicity of the Magellanic Clouds is similar to galaxies in the earlier epochs of the Universe, thus the presence of COMs in the LMC and SMC indicates that a similar prebiotic chemistry leading to the emergence of life, as it happened on Earth, is possible in lowmetallicity systems in the earlier Universe.