An unsteady model of droplet formation in co-flow and flow-focusing microfluidics is developed and numerically analyzed to investigate the dynamic behaviors of droplet formation in axisymmetric microfluidics with a focus on the role of local geometry. The effects of capillary number and local geometry on the droplet formation regimes, droplet sizes and monodispersity as well as droplet generation frequency are examined and analyzed. Once identified, a drop formation regime diagram is provided to quantitatively describe the respective regime of dripping, dripping-jetting transition, and jetting in axisymmetric microfluidics, depending on the Capillary number and orifice radius. The results indicate that, the existence of focusing orifice induces a strong hydrodynamic focusing effect, causing the droplet formation behaviors in flow-focusing microfluidics depart from the co-flow one. The dripping-jetting transition regime occurs at a smaller Capillary number in flow-focusing microfluidics, and the droplets produced by flow-focusing microfluidics are smaller than those in co-flow system with wider size distribution and higher frequency. Interestingly, the droplet formation in flow-focusing microfluidics is significantly affected by the orifice radius while it is insensitive to the orifice length. In addition, when the orifice radius is sufficiently small or the Capillary number is larger than 0.3, only the jetting regime is observed. As the orifice radius increases, the regions of Capillary number for both the dripping-jetting transition regime and dripping regime turn to be larger. (C) 2017 Elsevier Ltd. All rights reserved.