Industry 4.0 technologies are gaining traction with every aspect of modern manufacturing and distribution procedures. In the context of supply chain management, where the flow of products and information is of the utmost importance, these technologies play a crucial role in achieving accuracy, speed, and flexibility while being cost effective. A central node of each supply chain is the distribution center. The main functionalities of distribution centers concern receiving, storing, packaging and dispatching goods, while managing all necessary information related to them. The paper at hand provides a short yet representative literature survey for the Industry 4.0 technologies that have been adopted so far in the logistics applications of contemporary distribution centers. The standard processes are outlined and examined in terms of their automation with novel applied or theoretical technological solutions. In addition, the emerging processes of distribution centers are discussed including demand forecasting and automation in last-mile delivery. Discussions and future trends are also presented, and the adoption pace of the new technologies is analyzed.