Challenges to future EIS due to business, socio-economic, and ecological environment complexity.Fundamental limitations to the controllability of complex systems as a challenge to sustainability.Complexity management and complexity reduction methods.State of the art of promising relevant areas of computing and communication. The article provides an overview of the challenges and the state of the art of the discipline of Enterprise Architecture (EA), with emphasis on the challenges and future development opportunities of the underlying Information System (IS), and its IT implementation, the Enterprise Information System (EIS). The first challenge is to overcome the narrowness of scope of present practice in IS and EA, and re-gain the coverage of the entire business on all levels of management, and a holistic and systemic coverage of the enterprise as an economic entity in its social and ecological environment. The second challenge is how to face the problems caused by complexity that limit the controllability and manageability of the enterprise as a system. The third challenge is connected with the complexity problem, and describes fundamental issues of sustainability and viability. Following from the third, the fourth challenge is to identify modes of survival for systems, and dynamic system architectures that evolve and are resilient to changes of the environment in which they live. The state of the art section provides pointers to possible radical changes to models, methodologies, theories and tools in EIS design and implementation, with the potential to solve these grand challenges.