Liquid phase crystallization of silicon (LPC-Si) offers great potential for high-quality Si films and a cost effective fabrication technique for thin crystalline silicon solar cells on glass. In this work, we report on the progress on LPC-silicon at HZB in the past years. Beginning with a brief description of the fabrication process, we summarize the work on the different contact systems developed for these absorbers before focusing on the interdigitated back contact architecture on which the highest efficiencies were reported. State-of-the art cells form the basis for a detailed discussion of the status of this technology. We investigate the current loss mechanisms and explore the potential for further improvement. Finally, based on this comprehensive quality assessment, we develop a roadmap to increase the cell efficiencies to wafer-equivalent values.