The European FP7 project PEPPHER is addressing programmability and performance portability for current and emerging heterogeneous many-core archi- tectures. As its main idea, the project proposes a multi-level parallel execution model comprised of potentially parallelized components existing in variants suitable for different types of cores, memory configurations, input characteristics, optimization criteria, and couples this with dynamic and static resource and architecture aware scheduling mechanisms. Crucial to PEPPHER is that components can be made performance aware, allowing for more efficient dynamic and static scheduling on the concrete, available resources. The flexibility provided in the software model, combined with a customizable, heterogeneous, memory and topology aware run-time system is key to efficiently exploiting the resources of each concrete hardware configuration. The project takes a holistic approach, relying on existing paradigms, interfaces, and languages for the parallelization of components, and develops a prototype framework, a methodology for extending the framework, and guidelines for constructing performance portable software and systems ­ including paths to migration of existing software ­ for heterogeneous many-core processors. This paper gives a high-level project overview, and presents a specific example showing how the PEPPHER component variant model and resource-aware run-time system enable performance portability of a numerical kernel.