Emulsions are metastable dispersions in which molecular transport is a major mechanism driving the system towards its state of minimal energy. Determining the underlying mechanisms of molecular transport between droplets is challenging due to the complexity of a typical emulsion system. Here we introduce the concept of 'minimal emulsions', which are controlled emulsions produced using microfluidic tools, simplifying an emulsion down to its minimal set of relevant parameters. We use these minimal emulsions to unravel the fundamentals of transport of small organic molecules in water-in-fluorinated-oil emulsions, a system of great interest for biotechnological applications. Our results are of practical relevance to guarantee a sustainable compartmentalization of compounds in droplet microreactors and to design new strategies for the dynamic control of droplet compositions.