This article examines the existing confusion over the multiple leadership styles related to successful implementation of corporate social responsibility/sustainability in organisations. The researchers find that the problem is the complex nature of sustainability itself. We posit that organisations are complex adaptive systems operating within wider complex adaptive systems, making the problem of interpreting just in what way an organisation is to be sustainable, an extraordinary demand on leaders. Hence, leadership for sustainability requires leaders of extraordinary abilities. These are leaders who can read and predict through complexity, think through complex problems, engage groups in dynamic adaptive organisational change and have the emotional intelligence to adaptively engage with their own emotions associated with complex problem solving. Leaders and leadership is a key interpreter of how sustainability of the organisation 'links' to the wider systems in which the organisation sits, and executing that link well requires unusual leaders and leadership systems.