The paper is focused on the importance of business processes and its management in the concept of fourth industrial revolution and the introduction of group of emerging techniques supporting this field. In fact, the whole concept of the Industry 4.0 is laying on business processes. The management of the processes will have a significant impact on the value added, effectiveness and efficiency of organizations involved in the Industry 4.0. The process-centric approach is necessary not only for management of the manufacturing processes, but also for the management of non-manufacturing processes. The newly emerging group of techniques used in business process management as well suited tools for the management of the processes at the operational level is called process mining and we believe it might enhance Industry 4.0 in many of its aspects. The paper is structured as follows. In the first sections, we introduce the concept of Industry 4.0 and demonstrate the importance of processes for the concept. In next section, we introduce the group of techniques called process mining and in the closing section we demonstrate the usability of process mining. Finally, we present and discuss our results supporting the advantages of process mining and their suitability for Industry 4.0 idea.