Since their appearance, computer programs have embodied discipline and structured approaches and methodologies. Yet, to this day, equipping machines with imaginative and creative capabilities remains one of the most challenging and fascinating goals we pursue. Intelligent software agents can behave intelligently in well-defined scenarios, relying on Machine Learning (ML), symbolic reasoning, and their developers' capability of tailoring smart behaviors on the particular application domain(s). However, to forecast all possible scenarios’ evolutions is unfeasible. Thus, intelligent agents should autonomously/creatively adapt to the world’s mutability. This paper investigates the meaning of imagination in the context of cognitive agents, addresses techniques and approaches to let agents autonomously imagine/simulate their course of action and generate explanations supporting it, and formalizes thematic challenges. In particular, we investigated research areas such as: i) reasoning and automatic theorem proving (which is exploited to synthesize novel knowledge via inference), ii) automatic planning and simulation (which is exploited to speculate over alternative courses of action), iii) machine learning and data mining (which are exploited to induce new knowledge from experience), and (iv) biochemical coordination (which keeps imagination dynamic by continuously reorganizing it).