Recently it has become possible to probe individual excitons localized laterally in narrow GaAs quantum wells using high spatial and spectral resolution optical techniques. Discrete, atomic-like spectra with homogeneously-broadened linewidths as narrow as a few tens of micro-eV have been measured. These linewidths are two orders of magnitude narrower than the ensemble linewidth arising from inhomogeneous broadening and an order of magnitude narrower than the narrowest observed in wide quantum well samples. This extraordinary reduction in linewidth can be explained in part by the removal of inhomogeneous broadening accomplished by probing individual localized excitons, and in part by the reduction in homogeneous linewidth in going from 2D to 0D. In fact, the linewidths are in the regime expected for the intrinsic broadening mechanisms of exciton-phonon interactions and radiative emission. In other words the linewidths may be close to their natural linewidths.@footnote 1@ This great reduction in linewidth attained in PL by probing individual QDs has led to a number of new observations including fine structure splittings,@footnote 2@ hyperfine structure splittings @footnote 3@ and the measurement of the nonlinear response of a single quantum dot.@footnote 4@ Using coherent picosecond pulses, coherent control and the generation of superposition states have been demonstrated.@footnote 5@ These examples of advanced spectroscopies on individual excitons are first steps toward what may eventually lead in its maturity to coherent optical control of QDs comparable to what is now possible in atoms. @FootnoteText@ @footnote 1@ D. Gammon, et al., Science 273, 87 (1996). @footnote 2@ D. Gammon, et al., Phys. Rev. Lett. 76, 3005 (1996). @footnote 3@ S.W. Brown, et al., Phys. Rev. B 54, R17339 (1996); D. Gammon, et al., Science 277, 85 (1997). @footnote 4@ N. H. Bonadeo, et al., Phys. Rev. Lett. 81, 2759 (1998). @footnote 5@ N. H. Bonadeo, et al., Science 282, 1473 (1998).