Central Cantor sets form a class of symmetric Cantor sets of the realline. Here we give a complete characterization of the $C^{k +\alpha}$ regularityof these Cantor sets.We also give a classification of central Cantor sets up to global and localdiffeomorphisms. Examples of central Cantor sets with special dynamicaland measure-theoretical properties are also provided.Finally, we calculate the fractal dimensions of an arbitrary central Cantorset.