Drop formation and dripping and jetting phenomena occur in an extremely large variety of situation, spanning a broad range of physical length scales. In this paper, we study the dynamics of dripping-to-jetting transition for two immiscible coflowing liquid streams numerically. Two different classes of transition are identified. In both cases, nonlinear dynamical phenomena such as period doubling and chaos are observed between simple dripping and jetting. Extensive numerical calculations show that the first class of dripping-to-jetting transition is determined by the Weber number of the inner fluid Win, and the second class of dripping-to-jetting transition is controlled by capillary number of the outer fluid Cout.