Note: this answer is from a merged in question which was asking specifically about the chemistry of the creaming method.
The creaming of fat (typically butter or a hydrogenated vegetable shortening, such as the US brand Crisco) is more a mechanical process than a chemical one.
Sugar does not dissolve in fat, and pure shortening has no water to dissolve the sugar. Even butter is composed of no more than about 20% water, which may dissolve a small amount of sugar, but then will be saturated.
No significant chemical reactions are taking place during the creaming process.
The sugar crystals have very sharp edges. Under the agitation of the creaming, the sugar is forced into the fat mass, and the sharp edges cut into the fat phase small bubbles carrying air into the fat phase.
Because it is a mechanical process, you want the fat neither too cold (which makes it harder to mix), or too warm (when it will be so soft that it will collapse, and it is hard for the air pockets to be formed). Baking Info's article on the creaming method tells us the ideal temperature for creaming is 21°C (70°F).
When fully creamed, the mixture is a foam of sugar crystals and air in the primary fat phase. This air helps to leaven the baked good.
In many baking recipes, the next step after creaming sugar and fat is to emulsify eggs into the fat phase. This is also a mechanical process, as the egg proteins and liquids will form small drops throughout the butter phase. The additional water from the eggs will also continue to dissolve some of the sugars, but the product of this step is an emulsification of egg/water/syrup droplets and air pockets in a fat phase with sugar crystals embedded within it.