Semiconductor fabrication plants are subject to high levels of variability because of a variety of factors including re-entrant flows, multiple products, machine breakdowns, heterogeneous toolsets or batching processes. This variability decreases productivity, increases cycle times and severely impacts the systems tractability. Many authors have proposed approaches to better model the impact of variability, often focusing on specific aspects. We present a review of the sources of variability discussed in the literature and the methods proposed to manage them. We discuss their relative importance as seen by the authors as well as the limits current theories face. Finally, we emphasize the lack of research on some critical aspects related to High Mix Low Volume fabs. In this setting, the ability of practitioners to predict and anticipate the effects of changing product mix and client orders remains challenging, delaying the transition of semiconductor manufacturers towards Industry 4.0.