In this paper, we construct a complexity-based morphospace wherein one can study systems-level properties of conscious and intelligent systems based on information-theoretic measures. The axes of this space labels three distinct complexity types, necessary to classify conscious machines, namely, autonomous, cognitive and social complexity. In particular, we use this morphospace to compare biologically conscious agents ranging from bacteria, bees, C. elegans, primates and humans with artificially intelligence systems such as deep networks, multi-agent systems, social robots, AI applications such as Siri and computational systems as Watson. Given recent proposals to synthesize consciousness, a generic complexitybased conceptualization provides a useful framework for identifying defining features of distinct classes of conscious and synthetic systems. Based on current clinical scales of consciousness that measure cognitive awareness and wakefulness, this article takes a perspective on how contemporary artificially intelligent machines and synthetically engineered life forms would measure on these scales. It turns out that awareness and wakefulness can be associated to computational and autonomous complexity respectively. Subsequently, building on insights from cognitive robotics, we examine the function that consciousness serves, and argue the role of consciousness as an evolutionary game-theoretic strategy. This makes the case for a third type of complexity necessary for describing consciousness, namely, social complexity. Having identified these complexity types, allows for a representation of both, biological and synthetic systems in a common morphospace. A consequence of this classification is a taxonomy of possible conscious machines. In particular, we identify four types of consciousness, based on embodiment: (i) biological consciousness, (ii) synthetic consciousness, (iii) group consciousness (resulting from group interactions), and (iv) simulated consciousness (embodied by virtual agents within a simulated reality). This taxonomy helps in the investigation of comparative signatures of consciousness across domains, in order to highlight design principles necessary to engineer conscious machines. This is particularly relevant in the light of recent developments at the arXiv:1705.11190v3 [q-bio.NC] 24 Nov 2018The Morphospace of Consciousness 2 crossroads of cognitive neuroscience, biomedical engineering, artificial intelligence and biomimetics.