A surface is called a constant angle surface if its unit normal makes a constant angle with a "fixed" direction. Starting from this general definition, we give different choices of directions in order to study and classify constant angle surfaces. Firstly, in the Euclidean 3-space, one of the coordinates axes, the position vector field, or a Killing vector field may be chosen as a "fixed" direction. Secondly, recent classification results for constant angle surfaces in solvable Lie groups are obtained.