Additive manufacturing (AM) techniques enable new design concepts for performance improvements and functional integration in a wide range of industries. One promising application is in additively manufactured cutting tools for machining, improving process reliability on the one hand and increasing tool life and process productivity on the other hand. Compared to conventional manufacturing processes, AM allows for new and complex geometrical designs, enables the production of individualized parts, and offers new possibilities for alloy composition and material design. This work gives a comprehensive and systematic review of scientific as well as industrial activities, studies, and solutions regarding AM cutting tools and their fields of application. Four different areas are identified, including cooling and coolant supply, damping and vibrational behavior, lightweight design and topology optimization, and functional integration. Thus, the relevant and promising approaches for the industrialization of AM cutting tools are highlighted, and a perspective is given on where further scientific knowledge is needed.