We review our recent optical experiments on two-dimensional electron systems at temperatures below 1 K and under high magnetic fields. The two-dimensional electron systems are realized in modulation-doped GaAs-AlGaAs single quantum wells. Via gate electrodes the carrier density of the two-dimensional electron systems can be tuned in a quite broad range between about 1×10^{10} cm^{-2} and 2×10^{11} cm^{-2}. In dilute two-dimensional electron systems, at very low electron densities, we observe the formation of negatively charged excitons in photoluminescence experiments. In this contribution we report about the observation of a dark triplet exciton, which is observable at temperatures below 1 K and for electron filling factors <1/3, i.e., in the fractional quantum Hall regime only. In experiments where we have increased the density of the two-dimensional electron systems so that a uniform two-dimensional electron system starts to form, we have found a strong energy anomaly of the charged excitons in the vicinity of filling factor 1/3. This anomaly was found to exist in a very narrow parameter range of the density and temperature, only. We propose a model where we assume that localized charged excitons and a uniform Laughlin liquid coexist. The localized charged exciton in close proximity to the Laughlin liquid leads to the creation of a fractionally-charged quasihole in the liquid, which can account for the experimentally observed anomaly.