The temperature, the polarity of the solutes and solvent, the pressure, and the molecular size affect solubility. All of these factors play roles in determining which solutes dissolve in which solvents.
Temperature affects solubility by changing the properties of the solvent. As a general rule, as the temperature rises, the solubility rises. Polarity affects solubility because polar solvents dissolve polar solutes, and nonpolar solvents dissolve nonpolar solutes. Pressure only affects solubility for gases; the solubility of a gas is proportional to the pressure of the gas solvent. Molecular size affects solubility because larger molecules are more difficult to dissolve in solvents. Generally, smaller molecules dissolve more easily and are more soluble.