The first part of the talk discusses relativistic Coulomb excitation experiments performed at RCNP Osaka as a new tool to study the electric dipole polarizability of nuclei. Such data provide important constraints on the neutron skin thickness of nuclei and the equation of state of neutron-rich matter governing the properties of neutron stars. In the second part I present examples of nuclear structure investigations with electron scattering at the superconducting Darmstadt electron linear accelerator S-DALINAC and, in particular, the future program in the framework of a newly formed Collaborative Research Center.