We develop the basic spectral theory of ergodic Schrodinger operators when the underlying dynamics are given by a conservative
ergodic transformation of a \sigma-finite measure space. Some fundamental results, such as the Ishii--Pastur theorem carry over to the
infinite-measure setting. We also discuss some examples in which straightforward analogs of results from the probability-measure case do not hold. We will discuss some examples and some interesting open problems.
The talk is based on a joint work with M. Boshernitzan, D. Damanik, and M. Lukic.