Organic electrochemical transistors (OECTs) can be used to create biosensors, wearable devices and neuromorphic systems. However, restrictions in the micro- and nanopatterning of organic semiconductors, as well as topological irregularities, often limit their use in monolithically integrated circuits. Here we show that the micropatterning of organic semiconductors by electron-beam exposure can be used to create high-density (up to around 7.2 million OECTs per cm2) and mechanically flexible vertical OECT arrays and circuits. The energetic electrons convert the semiconductor exposed area to an electronic insulator while retaining ionic conductivity and topological continuity with the redox-active unexposed areas essential for monolithic integration. The resulting p- and n-type vertical OECT active-matrix arrays exhibit transconductances of 0.08-1.7 S, transient times of less than 100 mu s and stable switching properties of more than 100,000 cycles. We also fabricate vertically stacked complementary logic circuits, including NOT, NAND and NOR gates. Micropatterning of organic semiconductors by electron-beam exposure can be used to create vertical organic electrochemical transistor arrays and complementary logic circuits with densities of up to 7.2 million transistors per cm2.