Hydrogels are polymer networks infiltrated with water. Many biological hydrogels in animal bodies such as muscles, heart valves, cartilages, and tendons possess extreme mechanical properties including being extremely tough, strong, resilient, adhesive, and fatigue-resistant. These mechanical properties are also critical for hydrogels' diverse applications ranging from drug delivery, tissue engineering, medical implants, wound dressings, and contact lenses to sensors, actuators, electronic devices, optical devices, batteries, water harvesters, and soft robots. Whereas numerous hydrogels have been developed over the last few decades, a set of general principles that can rationally guide the design of hydrogels using different materials and fabrication methods for various applications remain a central need in the field of soft materials. This review is aimed at synergistically reporting: (i) general design principles for hydrogels to achieve extreme mechanical and physical properties, (ii) implementation strategies for the design principles using unconventional polymer networks, and (iii) future directions for the orthogonal design of hydrogels to achieve multiple combined mechanical, physical, chemical, and biological properties. Because these design principles and implementation strategies are based on generic polymer networks, they are also applicable to other soft materials including elastomers and organogels. Overall, the review will not only provide comprehensive and systematic guidelines on the rational design of soft materials, but also provoke interdisciplinary discussions on a fundamental question: why does nature select soft materials with unconventional polymer networks to constitute the major parts of animal bodies?