This paper focuses on mastering the automatic architecture synthesis and application mapping for heterogeneous massively-parallel MPSoCs based on customizable application-specific instruction-set processors (ASIPs). It presents an over-view of the research being currently performed in the scope of the European project ASAM of the ARTEMIS program. The paper briefly presents the results of our analysis of the main problems to be solved and challenges to be faced in the design of such heterogeneous MPSoCs. It explains which system, design, and electronic design automation (EDA) concepts seem to be adequate to resolve the problems and address the challenges. Finally, it introduces and briefly discusses the ASAM design-flow and its main stages