Nearly every cell type exhibits some form of polarity, yet the molecular mechanisms vary widely. Here we examine what we term 'chemical systems' where cell polarization arises through biochemical interactions in signaling pathways, 'mechanical systems' where cells polarize due to forces, stresses and transport, and 'mechanochemical systems' where polarization results from interplay between mechanics and chemical signaling. To reveal potentially unifying principles, we discuss mathematical conceptualizations of several prototypical examples. We suggest that the concept of local activation and global inhibition - originally developed to explain spatial patterning in reaction-diffusion systems - provides a framework for understanding many cases of cell polarity. Importantly, we find that the core ingredients in this framework - symmetry breaking, self-amplifying feedback, and long-range inhibition - involve processes that can be chemical, mechanical, or even mechanochemical in nature.