A novel numerical algorithm and modeling framework of a front tracking method based on adaptive anisotropic unstructured meshes for simulating two-phase interfacial flows is presented. In the traditional front tracking methods, a fixed uniform Eulerian Cartesian mesh is used for solving the fluid flow, and adaptive unstructured grid markers are used for tracking the phase-interface front. In the new algorithm, an adaptive anisotropic unstructured mesh is used for solving the fluid flow, as well as for tracking the phase-interface front. Special attentions are focused on developing an algorithm for physical variable interpolation between the two sets of unstructured meshes for both the fluid flow and the front movement. A modeling framework for the described numerical algorithm is implemented on the platform of the commercial CFD package ANSYS Fluent through user-defined functions. The advanced ANSYS Fluent fluid flow solver feature of using adaptive unstructured mesh is integrated with the front tracking method, which can handle complex boundary geometries and has high numerical efficiency. These advanced features are demonstrated through three numerical test examples of simulating a single gas bubble rising freely in a viscous liquid, a buoyancy-driven liquid droplet rising in a periodically constricted capillary tube, and a pressure-driven droplet passing through a small throat hole in a pipe. The accuracy of the simulation results is demonstrated through the comparison with those observed in experiments or obtained using other simulation methods. (C) 2019 Elsevier Ltd. All rights reserved.