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The increase of productivity and decrease of production loss is an important goal for modern industry to stay economically competitive. For that, efficient fault management and quick amendment of faults in production lines are needed. The prioritization of faults accelerates the fault amendment process but depends on preceding fault detection and classification. Data-driven methods can support fault management. The increasing usage of sensors to monitor machine health status in production lines leads to large amounts of data and high complexity. Machine Learning methods exploit this data to support fault management. This paper reviews literature that presents methods for several steps of fault management and provides an overview of requirements for fault handling and methods for fault detection, fault classification, and fault prioritization, as well as their prerequisites. The paper shows that fault prioritization lacks research about available learning methods and underlines that expert opinions are needed.