In this paper the complex systems are discussed from the business and economics point of view. It will be showed and motivated that social systems are typically chaotic and/or non-linear and therefore non-equilibrium or complex systems. It is discussed that the rapid change global consumer behaviour is underway, that further increases the complexity in the business and management. For successful management under complexity, a following principles are offered: openness and inte 8e0 rnational competition, tolerance and variety of the ideas, self-reliability and low dependence on external help. The paper discusses the opportunities and challenges in management under complexity from macro and micro economic perspective. It is motivated that small economies have good prospects to gain from the global processes underway, if they can demonstrate flexible production, reliable business ethics and good risk management. In this environment, the challenges for corporate managements are being also permanently changed: the balance between short term noise and long term chaos whose attractor includes customers, shareholders and employees must be found. The paper is concluded with the two financial applications: about debt and risk management. The non-equilibrium economic establishment leads to additional problems by using excessive borrowing; unexpected downturns in economy can more easily kill companies. Finally, the demand for quantitative improvements in risk management is postulated. Development of the financial markets has triggered non-linearity to spike in prices of various production articles such as agricultural and other commodities that has added market risk management to the business model of many companies.