The concept of almost periodicity is due to H. Bohr. The concept of rotation number is due to H. Poincaré. The Schrödinger operator is named after E. Schrödinger. In this talk, I will present our work on these topics, with a focus on introducing a rotation number in the spirit of Johnson and Moser for one-dimensional almost periodic Schrödinger operators with measure-valued potentials. This is joint work with David Damanik (Rice), Gang Meng(UCAS) and Meirong Zhang(Tsinghua).