Since its (re-)discovery in the second half of the 20th century, the lattice of corner-sharing triangles called kagome has become one of the key domains featuring paradigmatic models for exotic quantum electronic states of matter. Depending on the filling, the Hubbard model on the kagome lattice exhibits several fascinating phases subject to contemporary research in condensed matter physics, ranging from topological spin liquids over correlated Dirac metals and unconventional superconductivity to spin-type and charge-type Peierls phases as well as turbulent hydrodynamic flow. I will discuss recent progress in theory to understand such scenarios of correlated electron systems on the kagome lattice.