Cylindrical Algebraic Decomposition (CAD) is a classical construction in real algebraic geometry. The original cylindrical algebraic decomposition was proposed by Collins, using the classical elimination theory. In this talk, we will show a geometric approach to the cylindrical algebraic decomposition developed in a recent preprint by the speaker. Instead of polynomials, the central object in the new geometric theory is region. We relate the construction of CAD to the geometric fiber classification problem in algebraic geometry, which allows a new perspective using techniques like Grothendieck's Generic Freeness and Hermite's Quadratic Forms, and a new algorithm for Cylindrical Algebraic Decomposition is developed.