Hydrogels are being developed to bear loads. Applications include artificial tendons and muscles, which require high strength to bear loads and low hysteresis to reduce energy loss. However, simultaneously achieving high strength and low hysteresis has been challenging. This challenge is met here by synthesizing hydrogels of arrested phase separation. Such a hydrogel has interpenetrating hydrophilic and hydrophobic networks, which separate into a water-rich phase and a water-poor phase. The two phases arrest at the microscale. The soft hydrophilic phase deconcentrates stress in the strong hydrophobic phase, leading to high strength. The two phases are elastic and adhere through topological entanglements, leading to low hysteresis. For example, a hydrogel of 76 weight % water, made of poly(ethyl acrylate) and poly(acrylic acid), achieves a tensile strength of 6.9 megapascals and a hysteresis of 16.6%. This combination of properties has not been realized among previously existing hydrogels.