The ancient Greeks founded many scientific disciplines. But the Greeks generally believed every question could be answered just using logic, clever arguments, and maybe some divine revelation. Modern science still requires logic and cleverness but adds physical measurements and testing. The idea of doing experiments to test hypothesis was developed by Galileo, Bacon, and others in the 1600s. The power of the scientific method is clearly demonstrated by the incredible scientific advances of the last 500 years.
Conflict arises when either subject infringes on the other's domain.
Religion should deal with moral and spiritual issues, it should not make claims on physical laws or facts. Science should deal with physical laws, not claim moral or ethical knowledge. An explanation of how or why something happens. An untested model. No theory is ever accepted as absolute truth in science.