Uncertainty in the manufacturing environment can cause inefficient resource utilization and bottlenecks, leading to delays, increased costs, and energy consumption, which contradicts sustainable manufacturing practices. Minimal research has been done in exploring how different uncertainties leads to bottleneck in manufacturing and modelling them for system optimisation under uncertainty. This paper provides an extensive review of manufacturing bottlenecks, categorizing them into various types and examines the role of uncertainty—both internal and external—on the formation of bottlenecks. Moreover, the paper discussed the types of uncertainties found in manufacturing and the level to which they are categorized based on the information available. Various methods of modelling these uncertainties are discussed, including probability distributions, fuzzy logic, Bayesian networks, and grey system theory.  The applicable approaches for uncertainty management are discussed with their strengths and limitations. Furthermore, the paper sheds light on state-of-the-art optimization approaches that are used in uncertain environments, their strengths and limitations.  The paper also explores how Industry 4.0 technologies can help improve bottleneck management by introducing more resilient and adaptive solutions. Also, the role of Industry 4.0 technologies in modelling uncertain parameters and for optimization under uncertain manufacturing is discussed. It is concluded that managing these uncertainties effectively is critical for enhancing production efficiency and supporting sustainable practices in manufacturing. This paper can be used to select appropriate uncertainty modelling and optimization approaches to mitigate bottlenecks under uncertainty.