We study the jetting–dripping (J–D) transition of a flow-focused viscous liquid jet surrounded by a co-flowing immiscible, lower viscosity liquid. A theoretical model describing wave propagation in open cylindrical flows has been adapted to our problem and further expanded to incorporate spatio-temporal stability considerations (global modes). The J–D transition sets the minimum liquid flow rate issuing as a steady jet and breaking up into droplets whose size is commensurate with the jet diameter. At the onset of dripping, droplets become considerably larger than jetting droplets, under comparable flow parameters. A linear theory accounting for convective and absolute instability is provided, along with a detailed interpretation of the parametrical space, under realistic viscosity and density restrictions. The experimental part sums up a collection of laboratory data illustrating the J–D transition with good agreement with the theory.