The often touted attractive attributes of printed/organic electronics are its mechanically flexible form-factor, low-cost, green, on-demand printing, scalability, low-power operation, and intelligence (signal processing) ideally, the creation of intelligent lightweight electronics printed by simple ubiquitous printing processes, and integrated into new ways to exploit its mechanically flexible form-factor. Printed/Organic Electronics, now an industry on its own right and recognized as one of the key technological enablers for the Internet of Things, is largely complementary to silicon because the printed transistors are slow and the printed elements are large. The sanguine projected growth of the $29 B market today to $73 B by 2027 assumes that `intelligence' (analog, mixed-signal and digital signal processing) would be realizable. Nevertheless, many of the said attributes of printed/organic electronics remain a challenge. In this paper, we exemplify this with a comprehensive and critical review and tabulation of the state-of-the art printed digital, analog, and mixed-signal circuits. We further review the application space of printed/organic electronics and the supply chain, including their classifications and delineate the associated challenges in each constituent chain. These challenges, largely unresolved, are indeed formidable, and are discussed with a critical circuits and systems perspective. Our review depicts that contemporary design philosophies and methodologies for silicon are largely inadequate for printed/organic electronics. To this end, we discuss esoteric analog and digital design philosophies and methodologies, with emphasis on co-design and co-optimization between the different constituent supply chains that may potentially circumvent the said formidable challenges, and discuss the associated penalties thereto.