The rapid development of additive manufacturing, also known as three-dimensional (3D) printing, is driving innovations in both industry and academia. Direct ink writing (DIW), an extrusion-based 3D printing technology, can build 3D structures through the deposition of custom-made inks and produce devices with complex architectures, excellent mechanical properties, and enhanced functionalities. A paste-like ink is the key to successful printing. However, as new ink compositions have emerged, the rheological requirements of inks have not been well connected to printability, or the ability of a printed object to maintain its shape and support the weight of subsequent layers. In this review, we provide an overview of the rheological properties of successful DIW inks and propose a classification system based on ink composition. Factors influencing the rheology of different types of ink are discussed, and we propose a framework for describing ink printability using measures of rheology and print resolution. Furthermore, evolving techniques, including computational studies, high-throughput rheological measurements, machine learning, and materiomics, are discussed to illustrate the future directions of feedstock development for DIW. The goals of this review are to assess our current understanding of the relationship between rheological properties and printability, to point out specific challenges and opportunities for development, to provide guidelines to those interested in multi-material DIW, and to pave the way for more efficient, intelligent approaches for DIW ink development.

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