Due to increasing demand uncertainty and product variety, manufacturing systems must continually adapt to maintain productivity. Generally, decision-makers can maintain flexibility to account for these adaptations efficiently already in the design phase of manufacturing systems. Consequently, over the past few decades, a significant body of literature has addressed manufacturing system design associated with various manufacturing paradigms, claiming to provide the ‘right’ level of flexibility. Advanced analytical methods from Operations Research are frequently used in this domain to support decision-making. However, articles on the manufacturing paradigms remain in disjunct literature streams. In this article, we review literature from the last two decades that focuses on the application of Operations Research methods in manufacturing system design. The analyzed articles were selected from peer-reviewed scientific literature in a systematic search and screening process. To unite literature on different manufacturing paradigms, the concept of manufacturing flexibility is adapted, focusing on flexibility types required and considered in manufacturing systems’ design phases. The reviewed articles frequently employ mixed-integer linear programming or propose heuristic procedures. Most contributions evaluate static and deterministic settings, overlooking short- or long-term uncertainties in the design of manufacturing systems. Predominantly, flexibility is maintained to enhance economic or performance-oriented objectives. The consideration of social or ecological indicators, however, is barely found. Therefore, research perspectives from this analysis include integrating social and ecological indicators into multi-objective decision-making methods, anticipating neighboring planning problems during design, and applying systematic procedures to address uncertainty.