This master thesis shows the state of the art of the consolidation of thermoplastic composites and so one of the key steps in their processing. The focus is on the thereby occurring phenomena, the model concepts developed and the predictive power of these consolidation models. For this, the thesis is based on a comprehensive literature search and analysis of international research and development activities on the simulation of the consolidation process. Consolidation is therein first observed in general, detached from process specific aspects. The phenomena which occur in the course of consolidation namely laminate compaction, void dynamics, polymer healing as well as thermal aging, are explained and models developed to describe these are illustrated. Building on this, the specific aspects of the consolidation of continuous fiber reinforced thermoplastics (tapes, towpregs) are addressed. Achievement of good consolidation is especially challenging if it shall be reached in the course of continuously running processes. That is particularly the case with the continuous laying techniques. Therefore, a focus of this master thesis is on the continuously running thermoplastic laying and the thermoplastic welding processes. In this summarizing, systematic description of the current state of the art, special attention is dedicated to the issues of validity, significance and kind as well as degree of verification of the consolidation models developed. Finally a research map is derived. It identifies in particular the currently active research groups and introduces them briefly.