This work presents a computational methodology for the simulation of three-dimensional, two-phase flows, based on adaptive strategies for space discretization, as well as a varying time-step approach. The method is based on the Front-Tracking method and the discretization of the Eulerian domain employs a Structured Adaptive Mesh Refinement strategy along with an implicit-explicit pressure correction scheme. Modelling of the Lagrangian interface was carried out with the GNU Triangulated Surface (GTS) library, which greatly reduced the difficulties of interface handling in 3D. The methodology was applied to a series of rising bubble simulations and validated employing experimental results and compared to literature numerics. Finally, the algorithm was applied to the simulation of two cases of bubbles rising in the wobbling regime. The use of adaptive mesh refinement strategies led to physically insightful results, which otherwise would not be possible in a serial code with a uniform mesh. (C) 2013 Elsevier Ltd. All rights reserved.