Human organotypic and organoid cultures provide increasingly life-like models of tissue/organ development and disease, enable more realistic drug screening, and may ultimately pave the way for new therapies. A broad variety of extracellular matrix-based or inspired materials is instrumental in these approaches. In this review article, the foundations of the related materials design are summarized with an emphasis on the advantages and limitations of decellularized and reconstituted biopolymeric matrices as well as biohybrid and fully synthetic polymer hydrogel systems applied to enable specific organotypic and organoid cultures. Recent progress in the fabrication of defined hydrogel systems offering thoroughly tunable biochemical and biophysical properties is highlighted. Potentialities of hydrogel-based approaches to address the persisting challenges of organoid technologies, namely scalability, connectivity/integration, reproducibility, parallelization, and in situ monitoring are discussed.