Quasi-periodic Schrödinger operators possess a rich background in quantum physics. From a mathematical perspective, they are deeply connected to diverse fields such as dynamical systems, fractal geometry, harmonic analysis, and number theory. In this talk, I will survey recent advancements in the study of the spectral properties of quasi-periodic Schrödinger operators, with a particular emphasis on methodologies rooted in dynamical systems. This work is primarily collaborative, undertaken with A. Avila, Y. Last, M. Shamis, and J. You.