In the 1970s it was discovered that organic polymers, a class of materials otherwise best know as insulating plastics, could be made electronically conductive. As an alternative to silicon semiconductors, organic polymers offer many novel features, characteristics, and opportunities, such as producing electronics at low costs using printing techniques, using organic chemistry to tune optical and electronic properties, and mechanical flexibility. The conducting organic polymers have been used in a vast array of devices, exemplified by organic transistors, light-emitting diodes, and solar cells. Due to their softness, biocompatibility, and combined electronic and ionic transport, organic electronic materials are also well suited as the active material in bioelectronic applications, a scientific and engineering area in which electronics interface with biology. The coupling of ions and electrons is especially interesting, as ions serve as signal carriers in all living organisms, thus offering a direct translation of electronic and ionic signals. To further enable complex control of ionic fluxes, organic electronic materials can be integrated with various ionic components, such as ion-conducting diodes and transistors. This thesis reports a background to the field of organic bioelectronic and ionic devices, and also presents the integration of ionic functions into organic bioelectronic devices. First, an electrophoretic drug delivery device is presented, capable of delivering ions at high spatiotemporal resolution. The device, called the organic electronic ion pump, is used to electronically control amyloid-like aggregation kinetics and morphology of peptides, and offers an interesting method for studying amyloids in vitro. Second, various ion-conducting diodes based on bipolar membranes are described. These diodes show high rectification ratio, i.e. conduct ions better for positive than for negative applied voltage. Simple ion diode based circuits, such as an AND gate and a full-wave rectifier, are also reported. The AND gate is intended as an addressable pH pixel to regulate for example amyloid aggregation, while the full-wave rectifier decouples the electrochemical capacity of an electrode from the amount of ionic charge it can generate. Third, an ion transistor, also based on bipolar membranes, is presented. This transistor can amplify and control ionic currents, and is suitable for building complex ionic logic circuits. Together, these results provide a basic toolbox of ionic components that is suitable for building more complex and/or implantable organic bioelectronic devices.