The understanding of the electrons behavior and interactions in two-dimensional semiconductor heterostructures is the focus of our research. We do that using various optical spectroscopy techniques. Photo-luminescence measurements at low temperatures and high magnetic fields are used to determine the electrons energy spectrum. A special emphasis is given to the study of bound electron and hole complexes. Near-field scanning probe spectroscopy allows us to measure the local emission and absorption spectrum, and thereby obtain the local properties of the electron gas. Short pulse lasers allow us to study dynamical processes, such as energy and spin relaxation processes.