Over the past decade, methods to culture stem cells in three dimensions have opened up a plethora of new opportunities for basic and translational research in the life sciences. In particular, the use of natural extracellular matrix (ECM) surrogates, such as mouse tumour-derived Matrigel, unleashed the possibility to recapitulate complex multicellular behaviours in vitro, culminating in the successful derivation of miniaturized organs, termed organoids. While organoids hold tremendous potential as model systems in basic biology, the translational potential of these systems is hampered by their strict dependency on animal-derived matrices that suffer from batch-to-batch variability, potential immunogenicity, and ethical concerns. Recent efforts in engineering covalently crosslinked synthetic hydrogels have attempted to substitute these ill-defined organoid culture systems. However, although these bio-artificial matrices have shown significant potential for 3D organoid culture, their stability and their inherent elastic nature hamper organoid development. Indeed, the native ECM, just like Matrigel, is a highly viscoelastic and dynamic 3D milieu that can relax in response to tissue-induced stress by breaking and subsequently rearranging its network, thus permitting cellular remodelling without compromising the macroscopic stability of the material over time. Therefore, there is a need to develop the next generation of synthetic organoid culture matrices, exhibiting in vivo-like stress-relaxation properties. This thesis provides a perspective on how chemically defined, bio-inspired hydrogels can be designed as potential replacements for native ECM-based matrices for 3D organoid culture. In contrast to traditional synthetic hydrogels that cannot accommodate the dynamic mechanical changes occurring during organoid development, four types of synthetic matrices were developed that are crosslinked, either fully or partially, through dynamic physical bonds. The introduction of such network dynamics is shown to facilitate key morphogenetic processes, such as tissue budding, that are normally absent in purely elastic networks. A unifying hypothesis emerging from these results is that stress relaxation is a crucial requirement for 3D organoid culture. The mechanisms by which stress relaxation influence ISC fate and organoid development remain to be further studied. Preliminary experiments indicated that the stem cells may sense and respond to these characteristics through differential activation of mechanosensing pathways including the transcriptional co-activator YAP. The dynamic hydrogels developed in this thesis hold great promise as tunable environments for stem cell-based self-organization, enabling morphogenetic processes that may be suppressed in conventional synthetic hydrogels systems predominantly used in 3D cell culture applications.