The synthesis of organic compounds using polymer-supported catalysts, reagents, and/or scavengers, so that the required product is always in solution, has been of great interest in recent years, especially in connection with pharmaceutical research. To date, the reactions have almost always been carried out in batch mode. It is now timely to consider developing them further and carrying them out using flow systems. Advantages of flow systems typically include the following: there is little or no reaction workup, the support suffers no physical damage in use, automation is relatively easy, and extension to continuous production, even on a large scale, is a possibility. This paper gives a brief background on previous work using polymer-supported catalysts, reagents, and/or scavengers and then reviews in detail the work that has been done to date using these reactants in flow systems. It identifies some of the problems encountered and indicates how they might be solved. Rapid progress requires collaborations between organic chemists, polymer chemists, and chemical engineers.