Membraneless organelles are cellular compartments made from drops of liquid protein inside a cell. These compartments assemble via the phase separation of disordered regions of proteins in response to changes in the cellular environment and the cell cycle. Here we demonstrate that the solvent environment within the interior of these cellular bodies behaves more like an organic solvent than like water. One of the most-stable biological structures known, the DNA double helix, can be melted once inside the liquid droplet, and simultaneously structures formed from regulatory single-stranded nucleic acids are stabilized. Moreover, proteins are shown to have a wide range of absorption or exclusion from these bodies, and can act as importers for otherwise-excluded nucleic acids, which suggests the existence of a protein-mediated trafficking system. A common strategy in organic chemistry is to utilize different solvents to influence the behaviour of molecules and reactions. These results reveal that cells have also evolved this capability by exploiting the interiors of membraneless organelles.