The axisymmetric, dynamic breakup of a Newtonian liquid jet injected vertically into another immiscible Newtonian liquid at various Reynolds numbers is investigated here. The full transient from jet start‐up to breakup into drops was simulated numerically by solving the time‐dependent axisymmetric equations of motion and continuity using an algorithm based on the Volume of Fluid (VOF) method that was previously proven successful in simulations of steady‐state liquid jets (i.e., of the jet region close to the nozzle before breakup). The algorithm has been further refined here based on its performance on transient problems such as the solution of the free liquid–liquid capillary jet breakup problem. The comparison of the simulation results with previous experimental measurements of jet length under conditions where all forces, i.e., viscous, inertial, buoyancy, and surface tension, are important, can be judged satisfactory given the sensitive dependence of the results on details of the experimental setup that are not available. The comparison involves the jet length till breakup as well as the jet and drop shapes, often far from regular. In comparison with experiment, the results of the present numerical method show a greater sensitivity of the jet length to the Reynolds number than the best predictions previously available based on the linear stability analysis of the free liquid–liquid capillary jet breakup problem.