With the recent developments in cell cultures and biomimetic materials, there is growing evidence indicating that long-established two-dimensional (2D) cell culture techniques are slowly being phased out and replaced with three-dimensional (3D) cell cultures. This is due to the 3D cell cultures better mimicking the natural extracellular matrix (ECM) where cells are found. The emergence of self-assembled hydrogels as an ECM mimic has revolutionised the field owing to their ability to closely simulate the fibrous nature of the ECM. Here, we review recent progress in using hydrogels as biomimetic materials in 3D cell cultures, particularly supramolecular peptide hydrogels. With greater comprehension of the behaviour of cells in these hydrogels, a cell culture system that can be used in a wide array of 3D culture-based applications can be developed.