The Supply Chain has undergone major transformations due to the need to implement new Industry 4.0 technologies, such as Internet of Things, Big Data, Cyber-Physical Systems and Cloud Computing. Thanks to these technologies, as well as to their subsystems and components, full integration of the supply chain is becoming possible. However, it is observed that the real impacts of Industry 4.0 technologies, rather positive or negative, are not yet totally clear and identified. This paper aims to identify and present an analysis of the challenges and obstacles that Industry 4.0 technologies may cause in the Supply Chain. For this, the most relevant papers on the topic were selected and analyzed through a systematic literature review. Twenty challenges grouped into four macrogroups were identified: (1) technical challenges, (2) financial, environmental and legal challenges, (3) technological challenges, and (4) sociocultural challenges. It should be noted that these challenges require greater attention and more in-depth studies on the part of the academy to support industry in order to mitigate them and thus allow better use of the available technological resources and optimize the performance of Supply Chain operations.