Abstract Vertical slug flow is characterized by the rise of long bullet-shaped gas bubbles with a diameter almost matching that of the tube - Taylor bubbles. Liquid slugs separate consecutive Taylor bubbles, which may interact and coalesce if the distance between them is small. Slug flow has numerous industrial applications, being also observed on physiological and geological systems. In spite of the contribution of the development of non-intrusive experimental techniques to a deeper understanding of slug flow features, the complexity of this flow pattern requires the combined use of numerical approaches to overcome some of the optical problems reported in experimental methods, and other limitations related to the flow aperiodic behavior. The need to systematize the large amount of data published on the subject and to understand the limitations of the techniques employed constitutes the motivation for this review. In the present work, literature on vertical gas–liquid slug flow, with Newtonian fluids, from 1943 to 2015, covering theoretical, experimental and numerical approaches, is reviewed. Focus is given to single and trains of Taylor bubbles rising through stagnant and co-current liquids. It should be emphasized, however, that further research still needs to be conducted in some particular areas, namely the hydrodynamics of the liquid film surrounding the Taylor bubbles, the interaction between consecutive bubbles, and a more detailed approach to the flow of Taylor bubbles through co-current liquids.