The Supremacy Clause is defined in Article VI of the Constitution as giving the federal government priority in any case where state or local laws hinder legislation passed by Congress. According to HowStuffWorks, the federal government doesn't always flex its muscle over the doctrine of preemption, but when it does it can go all-out.
One recent example of the federal government exercising the Supremacy Clause to overturn a state-level law occurred in relation to the highly restrictive immigration bill Arizona passed in response to what the state perceived to be federal inaction on illegal immigration. The state argued that the law was complementary; that is, it only reinforced the federal laws against illegal entry. However, the Obama administration sued the state of Arizona, claiming that Arizona's actions conflicted with federal law. The case was heard by the Supreme Court in 2012 and, according to HowStuffWorks, the controversial law was partially struck down on supremacy grounds.
Sometimes, the federal government declines to prosecute possible violations of supremacy. Nevada, for example, permits prostitution in rural counties. This, HowStuffWorks explains, is a violation of federal law, but corrective action has never been taken to resolve the conflict. California's experiment with marijuana dispensaries has been a middle ground, with some federal raids being carried out but without a determined effort to shut down the entire industry.