The circular economy (CE) is a contemporary concept that includes the use of renewable materials and technologies, making sustainability an important part of corporate management. The paper deals with issues related to the current state of learning and management of the application of circular economy concepts—CE. The main purpose of this work is to identify both the interest of industries in the CE field in terms of the principles of eco-design and eco-innovation of sustainable industrial products, as well as the approach and development of the concept during the pandemic period. The authors performed a scientometric analysis in the Web of Science (WOS) database for the CE field, having two search criteria: sustainability and eco-design. As a result, 66 publications from the last five years were retained. Given the higher number of publications in the last three years, CE was found to be a topical area. Out of the 66 publications, using the PRISMA diagram, the authors identified the eligible articles, excluding 15 of them as being only tangential to the CE field and not applied in the industry. Depending on the high frequency of certain keywords, the authors identified three important directions for the CE approach that corroborate and interpret the results obtained: M—management (1); P—packing (2); and L—Learning (3). Following this approach, the authors determined the focus of the manufacturing industries in terms of applying the concepts and principles of CE, thus being able to contribute to the creation of eco-innovation and eco-design practices of industrial products, especially industrial packaging. The paper will also be beneficial for Ph.D. students who show a certain interest in CE and will help develop the following research directions in this field.