The operation of a piezo inkjet printhead involves a chain of processes in many physical domains at different length scales. The final goal is the formation of droplets of all kinds of fluids with any desired volume, velocity, and a reliability as high as possible. The physics behind the chain of processes comprise the two-way coupling from the electrical to the mechanical domain through the piezoelectric actuator, where an electrical signal is transformed into a mechanical deformation of the printhead structure. The next two steps are the coupling to the acoustic domain inside the ink channels, and the coupling to the fluid dynamic domain, i.e. the drop formation process. The dynamics of the printhead structure are coupled via the acoustics to the drop formation process in the nozzle. Furthermore, wetting of the nozzle plate and air bubbles can have a negative influence on the printhead performance. The five topics (actuation, channel acoustics, drop formation, wetting, and air bubbles) are reviewed in this paper. This research connects the product developments for many emerging new industrial applications of the inkjet technology to the fundamental physical phenomena underlying the printhead operation.