Hydrogels, as interconnected networks (polymer mesh; physically, chemically, or dynamic crosslinked networks) incorporating a high amount of water, present structural characteristics similar to soft natural tissue. They enable the diffusion of different molecules (ions, drugs, and grow factors) and have the ability to take over the action of external factors. Their nature provides a wide variety of raw materials and inspiration for functional soft matter obtained by complex mechanisms and hierarchical self-assembly. Over the last decade, many studies focused on developing innovative and high-performance materials, with new or improved functions, by mimicking biological structures at different length scales. Hydrogels with natural or synthetic origin can be engineered as bulk materials, micro- or nanoparticles, patches, membranes, supramolecular pathways, bio-inks, etc. The specific features of hydrogels make them suitable for a wide variety of applications, including tissue engineering scaffolds (repair/regeneration), wound healing, drug delivery carriers, bio-inks, soft robotics, sensors, actuators, catalysis, food safety, and hygiene products. This review is focused on recent advances in the field of bioinspired hydrogels that can serve as platforms for life-science applications. A brief outlook on the actual trends and future directions is also presented.