The Kubo-Anderson model is a stochastic model of phase relaxation of an ensemble of systems in a fluctuating environment. This model is usually studied under the assumption that the system-environment interaction is a Gaussian stochastic process. This assumption only holds if the environment changes a very large number of times on the time scale of the system's motion. This paper reviews our work on the Kubo-Anderson model for the case where this interaction is a continuous-time random walk. A continuous-time random walk is a simple model for a 'slowly changing environment', i.e., one which makes a relatively small number of changes on the time scale of the system's motion. We present the key results from this model and show how to apply them to common problems in magnetic resonance spectroscopy and and non-linear optical spectroscopy.