Traditional predator-prey models focus on various types of functional responses in predation mechanism which is direct effect of predator on prey, but ignore the fear effect which is indirect. Based on some recent field experimental studies, such an indirect effect can be as significant as the direct one. In this talk, I will report some of our recent results in modifying some predator-prey models by incorporating the prey's anti-predation responses due to fear of predators. Various types of responses are considered, including reducing the productions and increasing mobilities, leading to various types of differential equations. These results not only reveal some interesting phenomena in the trade-offs between benefits and cost resulted from the anti-predation responses, they also suggest a need of re-visiting many (if not all) existing predator-prey models.