Modern bioprinting techniques aim to replicate target tissues by extruding a gel containing stem cells into a predefined pattern and culturing it under specific conditions. The embedded cells utilize nutrients from the culture medium to grow and differentiate into specialized tissue structures. Our research focuses on theoretical and computational modeling to simulate the various stages of bioprinting-from planning to post-printing treatments [1]. The aim is to enable precise control over the multiple process variables that determine the success of the procedure and an effective multifunctional optimization of hydrogel response. In this work, we present recent advancements in the modeling of photon-assisted crosslinking mechanisms in bio-inks, with particular emphasis on their interaction with viscoelastic extrusion phenomena [2-4]. Additionally, we outline a modelling framework to investigate how the biophysical properties of the resulting polymer network influence cellular motility and nutrient diffusion [5, 6], providing insights into the broader implications for tissue engineering. References. [1] M. Conti, M. Marino. Bioprinting: From Multidisciplinary Design to Emerging Opportunities, Elsevier 2022. [2] A. Hajikhani, P. Wriggers, M. Marino, Chemo-mechanical modelling of swelling and crosslinking reaction kinetics in alginate hydrogels: A novel theory and its numerical implementation, Journal of the Mechanics and Physics of Solids 153, (2021). [3] F. Chirianni, G. Vairo, M. Marino, Development of process design tools for extrusion-based bio- printing: From numerical simulations to nomograms through reduced-order modeling, Computer Methods in Applied Mechanics and Engineering 419 (2024). [4] J.H. Urrea-Quintero, M. Marino, T. Wick, et al. A Comparative Analysis of Transient Finite- Strain Coupled Diffusion-Deformation Theories for Hydrogels, Arch Computat Methods Eng 31, 37673800 (2024). [5] P. Gaziano, M. Marino, A Phase-field model of cell motility in biodegradable hydrogel scaffolds for tissue engineering applications, Computational Mechanics 74(1), 45-66 (2024). [6] P. Gaziano, Marino, M. Computational modeling of cell motility and clusters formation in enzyme- sensitive hydrogels, Meccanica 59, 1335-1349 (2024).