New methodologies are needed for the development of avionics systems to meet today’s software explosion in complexity and related cost due to the increased functionality in the aircraft. Current design flows for software-intensive systems do not have a clear path from the functional specification to the final implementation and cannot provide real-time guarantees. The situation will become even more difficult because, in the future, more and more applications will share the same computation nodes and the network in a distributed hierarchical network-based system. In order to overcome the present situation, a novel methodology for a correct-by-construction design of safety-critical embedded avionics systems has been created and formulated within the Vinnova NFFP7 project CORRECT. Correct-by-construction design is a radical departure from current design practice, with the potential to decrease the verification costs for future systems significantly. The paper presents the underlying foundation of the methodology, its carefully selected ingredients, and discuss available results and existing tool support. The methodology is based on a disciplined system modelling environment grounded on a sound formal foundation, a design space exploration technique, and a clear path to hardware and software synthesis. An industrial case study investigates the potential of the methodology.