Abstract : The 3-year European FP7 project PEPPHER addresses efficient utilization and usage of hybrid (heterogeneous) computer systems consisting of multi-core CPUs with GPU-type accelerators. PEPPHER is concerned with two major aspects: programmability and efficiency on given heterogeneous systems, and code and performance portability between different heterogeneous systems. The PEPPHER approach is pluralistic and parallelization agnostic, aiming to support different parallel languages and frameworks at different levels of parallelism. The central idea of PEPPHER is to maintain multiple, tailored implementation variants of performance-critical components of the application and schedule these efficiently either dynamically or statically across the available CPU and GPU resources. Implementation variants are supplied incrementally by hand, by compilation, by component composition, by auto-tuning, or taken from expert-written, adaptive libraries. This paper outlines the PEPPHER performance aware component model, its means for performance prediction, the PEPPHER run-time system, and other major aspects of the project concerned with algorithm and data structure support, compilation, and hardware feedback. A larger example demonstrating performance portability with the PEPPHER approach across hybrid systems with one to four GPUs is discussed: each GPU that is added to the system brings a linear performance increase, and performance aware scheduling provides for more efficient utilization of the combined CPU-GPU resources.