Thermoelectric properties of low-dimensional charge-carrier systems in high-quality semiconductor heterostructures are studied experimentally and theoretically. The project focuses on systems, in which the energy spectrum is controllable to a high extent via external parameters. They can be viewed as model systems for the engineering of nanoscale objects and devices with tailored thermoelectric properties. Experiments are performed on two-dimensional systems, embedded in nanoscrolls, quasi-onedimensional wires as well as zero-dimensional coupled quantum dot systems in modulation doped III-V heterostructures. Device structures are prepared by means of electron-beam lithography. Consequences for the thermopower due to the coexistence of coherent and incoherent transport processes will be addressed in detailed theoretical studies.