  This article summarizes and extends the recent developments in the
microscopic modeling of the magnetic excitations in cuprate two-leg ladder
systems. The microscopic Hamiltonian comprises dominant Heisenberg exchange
terms plus an additional four-spin interaction which is about five times
smaller. We give an overview over the relevant energies like the one-triplon
dispersion, the energies of two-triplon bound states and the positions of
multi-triplon continua and over relevant spectral properties like spectral
weights and spectral densities in the parameter regime appropriate for cuprate
systems. It is concluded that an almost complete understanding of the magnetic
excitations in undoped cuprate ladders has been obtained as measured by
inelastic neutron scattering, inelastic light (Raman) scattering and infrared
absorption.
