Is artificial consciousness theoretically possible? Is it plausible? If so, is it technically feasible? To make progress on these questions, it is necessary to lay some groundwork clarifying the logical and empirical conditions for artificial consciousness to arise and the meaning of relevant terms involved. Consciousness is a polysemic word: researchers from different fields, including neuroscience, Artificial Intelligence, robotics, and philosophy, among others, sometimes use different terms in order to refer to the same phenomena or the same terms to refer to different phenomena. In fact, if we want to pursue artificial consciousness, a proper definition of the key concepts is required. Here, after some logical and conceptual preliminaries, we argue for the necessity of using dimensions and profiles of consciousness for a balanced discussion about their possible instantiation or realisation in artificial systems. Our primary goal in this paper is to review the main theoretical questions that arise in the domain of artificial consciousness. On the basis of this review, we propose to assess the issue of artificial consciousness within a multidimensional account. The theoretical possibility of artificial consciousness is already presumed within some theoretical frameworks; however, empirical possibility cannot simply be deduced from these frameworks but needs independent empirical validation. Analysing the complexity of consciousness we here identify constituents and related components/dimensions, and within this analytic approach reflect pragmatically about the general challenges that the creation of artificial consciousness confronts. Our aim is not to demonstrate conclusively either the theoretical plausibility or the empirical feasibility of artificial consciousness, but to outline a research strategy in which we propose that "awareness" may be a potentially realistic target for realisation in artificial systems.