In this report we give an overview of models and discretisation techniques for the simulation of multiphase flow in long pipelines. Due to the size of the pipelines we focus on one-dimensional models, which are derived from three-dimensional conservation laws for mass, momentum and energy. All discussed one-dimensional models are hyperbolic, the most accurate ones are also non-conservative. We discuss the Discontinuous Galerkin Finite Element Method, which is a discretisation technique suitable for hyperbolic models, together with additional methods to handle discontinuities and non-conservative models. We apply the DG-FEM discretisation to a commonly used two-phase flow model and verify the results using two test cases. Several test cases, however, fail when one of the phases vanishes. We propose several solutions to resolve this problem.