Spectroscopic measurements with low-temperature scanning tunneling microscopes have been used very successfully for studying not only individual atomic or molecular spins on surfaces but also complexly designed coupled systems. The symmetry breaking of the supporting surface induces magnetic anisotropy which lead to characteristic fingerprints in the spectrum of the differential conductance and can be well understood with simple model Hamiltonians. Furthermore, correlated many-particle states can emerge due to the interaction with itinerant electrons of the electrodes, making these systems ideal prototypical quantum systems. In this manuscript more complex bipartite and spin-chains will be discussed additionally. Their spectra enable to determine precisely the nature of the interactions between the spins which can lead to the formation of new quantum states which emerge by interatomic entanglement. Figure 1: (a) Schematic view of the tunneling process between the electrodes of an idealized tip and sample with their constant densities of states ρt and ρs, respectively: In addition to the elastic tunneling current, an inelastic channel may open at a bias |eV T | ≥ ε i with ε i as the energy difference between the ground and an excited internal state. Under this circumstances an electron crossing the barrier can change its quantum state by losing part of its energy and exciting an internal degree of freedom, for example, the spin orientation of an magnetic adsorbate on the surface. (b) Schematic differential conductance, dI/dV (upper curve) and dI 2 /d 2 V (lower curve), spectra of an inelastic tunneling process. Symmetrically around E F a step like structure at a bias voltage |eV T | = ε i is detected in the dI/dV curve. This is smeared out at non-zero temperature (dashed line) leading to peaks with a width of 5.4k B T in the dI 2 /d 2 V curve. Figure adapted from reference [17].