Flow organization into systems fast-flowing ice streams is a well-known feature of ice sheets. A quintessential aspect of these ice streams is that they can emerge spontaneously out of an otherwise uniform flow, self-organize in evenly spaced patterns, and switch on and off over time, with major implications for the mass balance of ice sheets. While these dynamics render ice streams fascinating, they are also deeply troublesome. In fact, our understanding of the physics driving them is far from complete, thus impeding attempts to model future ice sheet behavior numerically over timescales longer than a few decades. In this talk, I strip away much of the sophistication involved in `operational’ ice sheet simulation codes to look at the necessary ingredients to capture ice stream dynamics in minimal continuum models. I will first identify the basic feedbacks responsible for oscillations in streaming flow, and how natural variability in climate forcing affects them. I will then delve into the spatial dynamics of ice streams, outlining how flow localization into distinct streams may emerge as a fluid flow instability.