High-performance thermally insulating materials from renewable resources are needed to improve the energy efficiency of buildings. Traditional fossil-fuel-derived insulation materials such as expanded polystyrene and polyurethane have thermal conductivities that are too high for retrofitting or for building new, surface-efficient passive houses. Tailored materials such as aerogels and vacuum insulating panels are fragile and susceptible to perforation. Here, we show that freeze-casting suspensions of cellulose nanofibres, graphene oxide and sepiolite nanorods produces super-insulating, fire-retardant and strong anisotropic foams that perform better than traditional polymer-based insulating materials. The foams are ultralight, show excellent combustion resistance and exhibit a thermal conductivity of 15 mW m(-1) K(-1), which is about half that of expanded polystyrene. At 30 °C and 85% relative humidity, the foams retained more than half of their initial strength. Our results show that nanoscale engineering is a promising strategy for producing foams with excellent properties using cellulose and other renewable nanosized fibrous materials.