Slug flow is a highly complex type of flow with an unsteady nature. The prediction of pressure drop, heat, and mass transfer for such flow is often considered a difficult task. The chapter deals with steady slug flow. The chapter introduces several options of modeling the hydrodynamic parameters and pressure drop using a unified approach that is applicable for the vertical, horizontal, and inclined cases. The chapter also reviews transient phenomena in slug flow by illustrating an example of severe slugging in a pipeline-riser system. It is noted that heat transfer in slug flow is of major importance for practical applications. The treatment of the two-phase flow is usually considered as a two-phase mixture. The severe slugging that consists of one riser and one pipeline is one of the simplest example of slug flow under nonsteady conditions. The Boe criterion differentiates between steady and cyclic operations with two exceptions. At high liquid flow rates, a steady flow can also exist within the severe slugging region predicted by the Boe criterion. There is a region outside the Boe criterion that is in an unsteady state and leads to unsteady oscillations.