Vaccines that elicit broadly protective anti-influenza antibodies. Some vaccines comprise nanoparticles that display HA trimers from influenza virus on their surface. The nanoparticles are fusion proteins comprising a monomeric subunit (e.g., ferritin) joined to the stem region of an influenza HA protein. The fusion proteins self-assemble to form the HA-displaying nanoparticles. The vaccines comprise only the stem region of an influenza HA protein joined to a trimerization domain. Also provided are fusion proteins, and nucleic acid molecules encoding such proteins, and assays using nanoparticles of the invention to detect anti-influenza antibodies.