Awareness and self-awareness are two different notions related to knowing the environment and itself. In a general context, the mechanism of self-awareness belongs to a class of co-called "self-issues" (self-* or self-star): self-adaptation, self-repairing, self-replication, self-development or self-recovery. The self-* issues are connected in many ways to adaptability and evolvability, to the emergence of behavior and to the controllability of long-term developmental processes. Self-* are either natural properties of several systems, such as self-assembling of molecular networks, or may emerge as a result of homeostatic regulation. Different computational processes, leading to a global optimization, increasing scalability and reliability of collective systems, create such a homeostatic regulation. Moreover, conditions of ecological survival, imposed on such systems, lead to a discrimination between "self" and "non-self" as well as to the emergence of different self-phenomena. There are many profound challenges, such as understanding these mechanisms, or long-term predictability, which have a considerable impact on research in the area of artificial intelligence and intelligent systems.