Exact diagonalization is a powerful numerical technique for analysing static and dynamicalquantities in quantum many-body lattice models. It provides unbiased informationconcerning quantum numbers, energies and wavefunctions of the low-energy eigenstates foralmost any kind of microscopic model. The information about energies and quantumnumbers is particularly useful to detect possible spontaneous symmetry breaking atT = 0. We review some of the advances in the field of frustrated quantum magnets which havebeen possible thanks to detailed symmetry analysis of exact diagonalization spectra. Newresults concerning the kagome and star lattice Heisenberg antiferromagnets are presented.