The recent outbreak of the COVID-19 pandemic in 2020 reasserted the necessity of artificial lung membrane technology to treat patients with acute lung failure. In addition, the aging world population inevitably leads to higher demand for better artificial organ (AO) devices. Membrane technology is the central component in many of the AO devices including lung, kidney, liver and pancreas. Although AO technology has improved significantly in the past few decades, the quality of life of organ failure patients is still poor and the technology must be improved further. Most of the current AO literature focuses on the treatment and the clinical use of AO, while the research on the membrane development aspect of AO is relatively scarce. One of the speculated reasons is the wide interdisciplinary spectrum of AO technology, ranging from biotechnology to polymer chemistry and process engineering. In this review, in order to facilitate the membrane aspects of the AO research, the roles of membrane technology in the AO devices, along with the current challenges, are summarized. This review shows that there is a clear need for better membranes in terms of biocompatibility, permselectivity, module design, and process configuration.