We are exploring the quasi-particle- and the spin dynamics in semiconductor quantum structures. The materials of interest are either GaAs-AlGaAs quantum structures, like quantum wells or nanowires, or, two-dimensional crystals (transition-metal dichalcogenides), like MoS2, MoSe2, WS2, and WSe2, and their van-der-Waals heterostructures. As experimental techniques we are employing time- and spatially-resolved Kerr/Faraday rotation, time-resolved photoluminescence, Raman spectroscopy, and four-wave mixing. The experiments are typically carried out at low temperatures, and, optionally, in high magnetic fields.