There is a considerable interest within both academia and industry to develop improved computational fluid dynamic methods for gas-liquid flows in bubble columns in order to support their scale-up and optimal design. One main model limitation in current Eulerian two-fluid and multi-fluid models concerns adequate closure relations for turbulence in bubble-driven flows. This article highlights some special features of bubble-induced turbulence, discusses shortcomings of common concepts for closure of the liquid phase turbulence kinetic energy equation and presents an approach for development and validation of improved models. Some problematic issues related to the direct numerical simulation of bubble swarms in narrow bubble columns are also discussed.