In the era of Industry 4.0, 3D printing, or additive manufacturing (AM), has revolutionized product design and manufacturing across various sectors. This review explores the evolution of 3D printing technology and its impact on industrial innovation, highlighting advancements in aeronautics, the automotive industry, and biomedicine. Various AM processes, such as binder jetting, direct energy deposition, and powder bed fusion, and materials like metals, polymers, ceramics, and composites, are discussed. Innovations like high-speed sintering, continuous liquid interface production, and bioprinting demonstrate ongoing advancements. The potential of 3D printing in personalized medical applications is emphasized due to its flexibility in geometry and materials. Despite progress, challenges like standardization, material quality, recycling, sustainability, and economic feasibility hinder widespread adoption. Overcoming these challenges is crucial for optimizing 3D printing technologies, ensuring high-quality, efficient, and affordable production. The review also addresses the future prospects of 4D and 5D printing technologies and their potential applications in various industries. This overview underscores 3D printing’s role in shaping the future of manufacturing within the context of Industry 5.0, emphasizing human–machine collaboration and sustainability.