Natural organisms are made of different types of microcompartments, many of which are enclosed by cell membranes. For these organisms to display a proper function, the microcompartments must be selectively permeable. For example, cell membranes are typically permeable toward small, uncharged molecules such as water, selected nutrients, and cell signaling molecules, but impermeable toward many larger biomolecules. Here, it is reported for the first time dynamic compartments, namely surfactant‐stabilized double emulsions, that display selective and tunable permeability. Selective permeability is imparted to double emulsions by stabilizing them with catechol‐functionalized surfactants that transport molecules across the oil shell of double emulsions only if they electrostatically or hydrophobically attract encapsulants. These double emulsions are employed as semipermeable picoliter‐sized vessels to controllably perform complexation reactions inside picoliter‐sized aqueous cores. This thus far unmet level of control over the transport of reagents across oil phases opens up new possibilities to use double emulsion drops as dynamic and selectively permeable microcompartments to initiate and maintain chemical and biochemical reactions in picoliter‐sized cell‐mimetic compartments.