3D bioprinting technologies have the potential to revolutionize biomedical material production. However, scaling from laboratory prototypes to industrial production presents challenges in maintaining material consistency and reproducibility. To address these challenges, we introduce some computational approaches to support the printing of hydrogels. We integrate physics-based modeling, data-driven model-order reduction, and feedback control. A significant challenge of hydrogels bioprinting is ensuring consistent material properties across large-scale batches and achieving reproducibility and uniformity in the final products. In this work, we introduce some computational approaches comprising high-fidelity multiphysics models accounting for the hydrogel dynamics during printing \cite{Urrea2024a,Urrea2024b}. We discuss model order reduction techniques to enable parameter calibration and uncertainty quantification \cite{Agarwal2024}, and present a feedback control strategy to maintain a desired Degree of Crosslinking (DoC) \cite{Urrea2024b}. The reduced-order model (ROM) is employed to optimally tune the feedback controller parameters and enable real-time simulation. Numerical experiments demonstrate that the proposed control strategy allows the printing of hydrogels with different DoC. Controlling the DoC allows for tailoring hydrogels to specific applications in biomechanics \cite{Urrea2024b} Our work aims to advance the additive manufacturing of functional materials by leveraging computational approaches for digital twinning. The ultimate goal is a closed-loop system that consistently yields high-quality, functional hydrogel products, advancing the reliability of bioprinting for industrial-scale applications such as fabricating human tissue analogs.