Adhesives are made of polymers because, unlike other materials, polymers ensure good contact between surfaces by covering asperities, and retard the fracture of adhesive joints by dissipating energy under stress. But using polymers to 'glue' together polymer gels is difficult, requiring chemical reactions, heating, pH changes, ultraviolet irradiation or an electric field. Here we show that strong, rapid adhesion between two hydrogels can be achieved at room temperature by spreading a droplet of a nanoparticle solution on one gel's surface and then bringing the other gel into contact with it. The method relies on the nanoparticles' ability to adsorb onto polymer gels and to act as connectors between polymer chains, and on the ability of polymer chains to reorganize and dissipate energy under stress when adsorbed onto nanoparticles. We demonstrate this approach by pressing together pieces of hydrogels, for approximately 30 seconds, that have the same or different chemical properties or rigidities, using various solutions of silica nanoparticles, to achieve a strong bond. Furthermore, we show that carbon nanotubes and cellulose nanocrystals that do not bond hydrogels together become adhesive when their surface chemistry is modified. To illustrate the promise of the method for biological tissues, we also glued together two cut pieces of calf's liver using a solution of silica nanoparticles. As a rapid, simple and efficient way to assemble gels or tissues, this method is desirable for many emerging technological and medical applications such as microfluidics, actuation, tissue engineering and surgery.