Supramolecular hydrogels are 3D, elastic, water-swelled materials that are held together by reversible, non-covalent interactions, such as hydrogen bonds, hydrophobic, ionic, host–guest interactions, and metal–ligand coordination. These interactions determine the hydrogels’ unique properties: mechanical strength; stretchability; injectability; ability to self-heal; shear-thinning; and sensitivity to stimuli, e.g., pH, temperature, the presence of ions, and other chemical substances. For this reason, supramolecular hydrogels have attracted considerable attention as carriers for active substance delivery systems. In this paper, we focused on the various types of non-covalent interactions. The hydrogen bonds, hydrophobic, ionic, coordination, and host–guest interactions between hydrogel components have been described. We also provided an overview of the recent studies on supramolecular hydrogel applications, such as cancer therapy, anti-inflammatory gels, antimicrobial activity, controlled gene drug delivery, and tissue engineering.