The negatively charged quasi-two-dimensional exciton ($X^-$) is studied numerically in the presence of a uniform B-field and various in-plane confinements. The corresponding photoluminescence (PL) spectra, including shakeup processes, are calculated. These calculations provide a quantitative explanation of recent experimental PL spectra. The photoluminescence signatures of charged excitons in quantum dots are also examined. Electron-hole pair distriution functions are calculated which show the structure of the charged exciton states (both ground and excited states). Increasing excitation reflects a competition between two effects: partial ionization of either one or two electrons.