Numerous cell functions require self organized polarity, e.g. cells must form a "front" and "back". Examples include motility (which I will primarily discuss), division, and neuronal growth. In some cases this polarity can form spontaneously and in others sufficiently large stimuli are required. In yet other cases, polarity determinants exhibit highly dynamic wave like behavior. Furthermore, individual cells can transition between these distinct behaviors. I will first discuss a joint modeling / experimental study that sheds light on the dichotomy between spontaneous and stimulus induced polarization, and describes how a cell might modulate its sensitivity to the external environment. I will then build on these results and discuss a unifying regulatory mechanism capable of giving rise to all three distinct polarity phenotypes. Additionally I will discuss related work on linking internal biochemical polarity dynamics to behavior and aggressiveness of melanoma cells.