Cell polarization, in which intracellular substances localize to a particular spot in response to external stimuli or internal cues, is central to cell physiology, and it underlies processes such as cell motility, cell division and cell differentiation. In this talk, I will present our recent works, using budding yeast as a model system, on how cells initiate symmetry breaking preceding the new bud emergence or mating projection. Along with experimental data, our mathematical modeling and simulations reveal potential mechanisms which underlie a biased cell polarity and pheromone concentration dependent cell morphology.