The design and synthesis of double network (DN) hydrogels that can mimic the properties and/or structure of natural tissue has flourished in recent years, overcoming the bottlenecks of mechanical performance of single network hydrogels and extending their potential applications in various fields. In recent years, such bioinspired DN hydrogels with extraordinary mechanical performance, excellent biocompatibility, and considerable strength have been demonstrated to be promising candidates for biomedical applications, such as tissue engineering and biomedicine. In this minireview, we provide an overview of the recent developments of bioinspired DN hydrogels defined as DN hydrogels that mimic the properties and/or structure of natural tissue, ranging from, e.g., anisotropically structured DN hydrogels, via ultratough energy dissipating DN hydrogels to dynamic, reshapable DN hydrogels. Furthermore, we discuss future perspectives of bioinspired DN hydrogels for biomedical applications.