Bubbly flows comprise a large number of different flow situations, e.g., dispersed pipe flows, flows in multiphase agitated tanks, flows in multiphase fixed-and fluidized-bed reactors, and typical bubble-column and loop-reactor flows. This paper focuses on bubble-driven flows. These are flow situations were the bubble movement itself is the main source of momentum to the now field and are often characterized by low superficial liquid velocities, relatively high superficial gas velocities, and no mechanical support of the now (e.g., agitation). Only vertical now situations are considered. An overview of the verified forces acting on bubbles is given, and examples of both classical and more recent modeling approaches are shown. This include gravity, buoyancy, centrifugal forces, conventional Magnus and Saffman forces, form and friction drag, and added mass as well as turbulent migration and other instability mechanisms. Special emphasis is placed on mechanisms creating bubble movement in the radial direction. Important literature on the subject with regard to the use of computational fluid dynamics to model gas-driven bubbly flows is reviewed, and the various approaches are evaluated, i.e., dynamic vs steady-state descriptions and Euler/Lagrange vs Euler/Euler formulations. Results from steady-state Euler/Euler simulations are given and discussed, and the demand for amplified modeling including more accurate and stable numerical solution schemes and algorithms is stressed.