During continuous composite extrusion, endless elements, such as steel wires, are embedded in the aluminum base material. Due to the complex material flow conditions, the design of composite extrusion dies is challenging. Therefore, numerical simulations are applied in order to determine appropriate die geometries and process parameters. In this paper, an overview of different modeling approaches for the simulation of continuous composite extrusion, which have been developed at the Institute of Forming Technology and Lightweight Construction (IUL) in recent years, is presented. In particular, fundamental differences of the methods are related to the utilized finite element approaches, i.e. the Eulerian formulation and the Lagrangian formulation. Furthermore, it is discussed whether it is necessary to consider the embedded elements physically in the simulation model. The advantages, drawbacks, and limits of the different approaches are presented, in particular with regard to material flow, reinforcing element position in the profile, and load on reinforcing elements. Furthermore, the simulation results are compared with experiments.