The main goal of the ANTAREX project is to express by a Domain Specific Language (DSL) the application self-adaptivity and to runtime manage and autotune applications for green and heterogeneous High Performance Computing (HPC) systems up to the Exascale level. Key innovations of the project include the introduction of a separation of concerns between self-adaptivity strategies and application functionalities. The DSL approach will allow the definition of energy-efficiency, performance, and adaptivity strategies as well as their enforcement at runtime through application autotuning and resource and power management.