The effect of pressure, temperature, and melt composition on CO2 and H2O solubilities in aluminosilicate melts, coexisting with CO2-H2O fluids, is discussed on the basis of previously published and new experimental data. The datasets have been chosen so that CO2 and H2O are the main fluid components and the conclusions are only valid for relatively oxidizing conditions. The most important parameters controlling the solubilities of H2O and CO2 are pressure and composition of melt and fluid. On the other hand, the effect of temperature on volatile solubilities is relatively small. At pressures up to 200 MPa, intermediate compositions such as dacite, in which both molecular CO2 and carbonate species can be dissolved, show higher volatile solubilities than rhyolite and basalt. At higher pressures (0.5 to 1 GPa), basaltic melts can incorporate higher amounts of carbon dioxide (by a factor of 2 to 3) than rhyolitic and dacitic melts. Henrian behavior is observed only for CO2 solubility in equilibrium with H2O-CO2 fluids at pressures < 100 MPa, whereas at higher pressures CO2 solubility varies nonlinearly with CO2 fugacity. The positive deviation from linearity with almost constant CO2 solubility at low water activity indicates that dissolved water strongly enhances the solubility Of CO2. Water always shows non-Henrian solubility behavior because of its complex dissolution mechanism (incorporation of OH-groups and H2O molecules in the melt). The model of Newman and Lowenstern (2002), in which ideal mixing between volatiles in both fluid and melt phases is assumed, reproduces adequately the experimental data for rhyolitic and basaltic compositions at pressures below 200 MPa but shows noticeable disagreement at higher pressures, especially for basalt. The empirical model of Liu et al. (2004) is applicable to rhyolitic melts in a wide range of pressure (0-500 MPa) and temperature (700-1200 degrees C) but cannot be used for other melt compositions. The thermodynamic approach of Papale (1999) allows to calculate the effect of melt composition on volatile solubilities but needs an update to account for more recent experimental data. A disadvantage of this model is that it is not available as a program code. The review indicates a crucial need of new experimental data for scarcely investigated field of pressures and fluid compositions and new models describing evident non-ideality of H-C-O fluid solubility in silicate melts at high pressures.