We shall review basic properties of cocycles over a minimal dynamical system, taking values in the special linear group of two by two matrices over the real numbers. It turns out that dynamical properties of such cocycles play a central role in the spectral theory of quasiperiodic one-dimensional Hamiltonians. We shall review those dynamical properties and connections with spectral theory. This talk will be of expository nature, and technical details will be kept to a minimum (respectively, we shall assume no prior background in the subject).