The distributed and heterogeneous nature of the data sources in High Performance Big Data Analytics (HPDA) applications, as well as the required computational power, is pushing designers towards novel computing systems that combine HPC, Cloud, and IoT solutions (for efficient and distributed computation closer to the data) with Artificial Intelligence (AI) algorithms (for knowledge extraction and decision making). In this context, the EVEREST project addresses the matching problem between application (and data) requirements, and the characteristics of the underlying heterogeneous hardware. Only an optimal match leads to efficient computation. In particular, we forecast that the creation of future Big Data systems will be of course data-driven, but also featuring complex heterogeneous and reconfigurable architectures that must be redesigned or customized based on the nature and locality of the data, and the type of learning/decisions to be performed. The EVEREST project aims at developing a holistic approach for co-designing computation and communication in a heterogeneous, distributed, scalable and secure system for HPDA. This is achieved by simplifying the programmability of heterogeneous and distributed architectures through a “data-driven” design approach, the use of hardware-accelerated AI, and through an efficient monitoring of the execution with a unified hardware/software paradigm. EVEREST proposes a design environment that combines state-of-the-art, stable programming models, and emerging communication standards, with novel and dedicated domain-specific extensions. Three industry-relevant application scenarios are used to validate the EVEREST approach and act as business cases for the project exploitation: (i) a weather analysis-based prediction model for the renewable energy trading market, (ii) an application for air-quality monitoring of industrial sites, and (iii) a real-time traffic modeling framework for intelligent transportation in smart cities.