My car’s gearbox refused to select reverse recently. I had to push the car out of a parking space after selecting neutral. The workshop says its “mechatronic module” had to be replaced. It was costly but, fortunately, the car was still under warranty. What is the function of this unit and why does it cost so much?

In a transmission, the mechatronic module consists of hydraulic pumps and actuators which are electronically controlled. Hydraulic oil pressure is what moves the actuators that shift the gears or select the clutch while the electronic controller is responsible for maintaining precision and high-speed function. 

Failure of either the mechanical or electronic network will result in some or all functions of the gearbox ceasing. In your case, the R or reverse function had shut down, possibly because of a weak hydraulic pump, leaking actuator or a broken valve.

Most automotive mechatronic modules are rarely serviceable and require a complete replacement in the event of a malfunction. Often, they are sealed units which cannot even be disassembled. The cost of a component hinges on its complexity. Or perhaps, also on its serviceability.