  In this survey we discuss spectral and quantum dynamical properties of
discrete one-dimensional Schr\"odinger operators whose potentials are obtained
by real-valued sampling along the orbits of an ergodic invertible
transformation. After an introductory part explaining basic spectral concepts
and fundamental results, we present the general theory of such operators, and
then provide an overview of known results for specific classes of potentials.
Here we focus primarily on the cases of random and almost periodic potentials.
