It is proposed that phenomenal awareness, the ability to be aware of one's sensations and feelings, emerges from the capacity of evolved brains to analyze their own cognitive processes by iterating and reapplying on them-selves the very same cortical operations that they use for the interpretation of signals from the outer world. Search for the neuronal substrate of awareness therefore converges with the search for the cognitive mechanisms through which brains analyze their environment. The hypothesis is put forward that the mammalian brain generates continuously highly dynamic states that, when modulated by input signals, rapidly converge towards points of transient stability that correspond to the respective input constellation. It is proposed that these states are characterized by the dynamic binding of feature-specific cells into functionally coherent cell assemblies which as a whole represent the constellation of features defining a particular perceptual object. Arguments are presented that favor the notion that the cognitive operations supporting awareness consist of an iteration of such dynamic binding processes which then lead to the formation of higher-order assemblies that correspond to the contents of conscious awareness. Experimental data are reviewed relating to the questions of how assemblies are formed and which signatures define the relations among the responses of distributed neurons. It is argued that assemblies self-organize through reciprocal interactions of neurons coupled by reentrant loops and that the signature of relatedness consists of the transient synchronization of the discharges of the respective neurons. Evidence is presented that these synchronization phenomena depend on the same state variables as awareness: Both require for their manifestation activated brain states characterized by desynchronized EEGs. It is concluded that phenomenal awareness is amenable to neurobiological reductionism; but it is also proposed that self-consciousness requires a different explanatory approach because it emerges from the dialogue between different brains and hence has the quality of a cultural construct.