This review explores additive manufacturing (AM) for refractory tungsten (W) and its alloys, highlighting the primary challenges and determining factors in the AM of pure W, W alloys and composites. The challenges mainly arise from W’s high melting point, low laser absorptivity, high thermal conductivity, high melt viscosity, high oxygen affinity, high ductile-to-brittle transition temperature, and inherent embrittlement, which lead to defects and anomalies in AM-produced parts. This review focuses on both processes and alloying strategies to address the issues related to densification, micro-cracking, and the resultant properties in W-based components. Cracking in additively manufactured W remains a persistent issue due to thermal stress, embrittlement, and oxide formation. Powder characteristics, process parameters, and thermal management strategies are crucial for W densification. Throughout the review, existing knowledge and insights are organized into comprehensive tables, serving as valuable resources for researchers delving deeper into this topic. Future research in W-AM should focus on understanding the interaction between AM process parameters and microstructural and material design. Advances in atomic-level understanding, thermodynamic modeling, and data analytics have the potential to significantly enhance the precision, sustainability, and applicability of W-AM.