The realization of biomimetic microenvironments for cell biology applications such as organ-on-chip, in vitro drug screening, and tissue engineering is one of the most fascinating research areas in the field of bioengineering. The continuous evolution of additive manufacturing techniques provides the tools to engineer these architectures at different scales. Moreover, it is now possible to tailor their biomechanical and topological properties while taking inspiration from the characteristics of the extracellular matrix, the three-dimensional scaffold in which cells proliferate, migrate, and differentiate. In such context, there is therefore a continuous quest for synthetic and nature-derived composite materials that must hold biocompatible, biodegradable, bioactive features and also be compatible with the envisioned fabrication strategy. The structure of the current review is intended to provide to both micro-engineers and cell biologists a comparative overview of the characteristics, advantages, and drawbacks of the major 3D printing techniques, the most promising biomaterials candidates, and the trade-offs that must be considered in order to replicate the properties of natural microenvironments.