Abstract The dynamic response of electron systems confined in a one-dimensional parabolic potential is investigated experimentally. Such structures are realized in so-called parabolic quantum wells where the parabolic confining potential is achieved by a proper grading of the barriers of a AlGaAs/GaAs quantum well. We present some of our recent studies on both intra- and interband fundamental excitations of such systems like cyclotron resonance. intersubband resonance, plasmon modes and photoluminescence excitations using various experimental techniques and geometries. Detailed studies of the electronic excitations in parabolic wells with intentionally induced deviations from ideal parabolicity allow for a better understanding of the effect of non-parabolic terms in the confining potential also for lateral nanostructures. Due to the simplicity of the confining potentials most of our experimental results can be explained in simple straightforward and transparent ways that also apply to recent investigations of lateral nanostructures and thus may serve for a better understanding also of this rapidly developing field.