In spite of interesting features as flexibility, organic thin-film transistors have commercially lagged behind due to the low mobilities of organic semiconductors associated with hopping transport. Furthermore, organic transistors usually have much larger channel lengths than their inorganic counterparts since high-resolution structuring is not available in low-cost production schemes. Here, we present an organic permeable-base transistor (OPBT) which, despite extremely simple processing without any high-resolution structuring, achieve a performance beyond what has so far been possible using organic semiconductors. With current densities above 1 kA cm−2 and switching speeds towards 100 MHz, they open the field of organic power electronics. Finding the physical limits and an effective mobility of only 0.06 cm2 V−1 s−1, this OPBT device architecture has much more potential if new materials optimized for its geometry will be developed.