Microfluidics have enabled notable advances in molecular biology^1,2, synthetic chemistry^3,4, diagnostics^5,6 and tissue engineering⁷. However, there has long been a critical need in the field to manipulate fluids and suspended matter with the precision, modularity and scalability of electronic circuits^8,9,10. Just as the electronic transistor enabled unprecedented advances in the automatic control of electricity on an electronic chip, a microfluidic analogue to the transistor could enable improvements in the automatic control of reagents, droplets and single cells on a microfluidic chip. Previous works on creating a microfluidic analogue to the electronic transistor^11,12,13 did not replicate the transistor’s saturation behaviour, and could not achieve proportional amplification¹⁴, which is fundamental to modern circuit design¹⁵. Here we exploit the fluidic phenomenon of flow limitation¹⁶ to develop a microfluidic element capable of proportional amplification with flow–pressure characteristics completely analogous to the current–voltage characteristics of the electronic transistor. We then use this microfluidic transistor to directly translate fundamental electronic circuits into the fluidic domain, including the amplifier, regulator, level shifter, logic gate and latch. We also combine these building blocks to create more complex fluidic controllers, such as timers and clocks. Finally, we demonstrate a particle dispenser circuit that senses single suspended particles, performs signal processing and accordingly controls the movement of each particle in a deterministic fashion without electronics. By leveraging the vast repertoire of electronic circuit design, microfluidic-transistor-based circuits enable fluidic automatic controllers to manipulate liquids and single suspended particles for lab-on-a-chip platforms.