While some are currently debating whether time may or may not be an illusion, others keep devoting their time to the science of consciousness. Time as such may be seen as a physical or a subjective variable, and the limitations in our capacity of perceiving and analyzing temporal order and change in physical events definitely constrain our understanding of consciousness which, in return, constrains our conceptual understanding of time. Temporal codes generated in the brain have been considered as the key to insight into neural function and, ultimately, as potential neural substrates of consciousness itself. On the basis of current evidence and opinion from neuroscience and philosophy, we consider the interrelation between consciousness and time in the light of Hegel and Heidegger's concepts of Sein (Being) and Zeit (Time). We suggest that consciousness can be defined in terms of a succession of psychological moments where we realize that we exist in, and are part of, a present moment in time. This definition places all other perceptual or sensorial processes which may characterize phenomenal experience at a different level of analysis and centers the debate around consciousness on the fundamental identity link between awareness of the Ich (I) and awareness of what Heidegger termed Ursprüngliche Zeit (original time). We argue that human consciousness has evolved from the ability to be aware of, to remember, and to predict temporal order and change in nature, and that the limits of this capacity are determined by limits in the functional plasticity of resonant brain mechanisms. Although the conscious state of the Self is the ultimate expression of this evolution, it is devoid of any adaptive function as such.