Lattice geometry, topological electron behaviour and the competition between different possible ground states all play a role in determining the properties of materials with a kagome lattice structure. In particular, the compounds KV3Sb5, CsV3Sb5 and RbV3Sb5 all feature a kagome net of vanadium atoms. These materials have recently been shown to exhibit superconductivity at low temperature and an unusual charge order at high temperature, revealing a connection to the underlying topological nature of the band structure. We highlight these discoveries, place them in the context of wider research efforts in topological physics and superconductivity, and discuss the open problems for this field.Superconductivity and ordered states formed by interactions—both of which could be unconventional—have recently been observed in a family of kagome materials.