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This paper compiles selected predictive analytical and numerical tools which can be used to model and understand the mechanisms of importance at different stages during and immediately after extrusion-based 3D printing of cementitious materials. The proposed toolbox covers different aspects of the process including mixing, material transportation, layer deposition, mechanical behavior of the fresh printed structure, and its early curing. Specifically, the paper provides basic analytical methods that should be helpful for an initial, first-order analysis of a given printing process. These methods deliver, in turn, a first estimation of some material requirements and process parameters. Limitations of these analytical methods are also discussed. Furthermore, the paper presents a review of advanced numerical tools that can be used to simulate the steps in the printing process accurately. It is shown that these tools can serve to describe complex behaviors, help in designing process parameters, or optimizing the rheological response, even though further developments are still needed to capture fully the attendant physical mechanisms. [ABSTRACT FROM AUTHOR]