The Harper's model describes Bloch electrons on a 2D lattice under a constant magnetic field. The mathematical study of Harper's model led to the development of spectral theory of the almost Mathieu operator.     In this talk, we will discuss recent progress  in the study of the  sharp arithmetic  spectral transition for almost Mathieu operators in the  positive Lyapunov exponent regime, distinguishing between singular continuous and pure  point spectra. We have also uncovered the universal hierarchical structure for the eigenfunctions in the pure point spectrum regime.  The talk is based on several papers, mainly  joint with Svetlana Jitomirskaya.