Higher ranked Marines (admirals and the fleet admiral) are expected to be on call to lead the Marine forces into war. This may take form of apprehending many criminals at once, protecting the World Nobles or calling a Buster Call to tackle a situation. Vice admirals are the ones who serve on the ships that the admirals call out and are tasked with carrying out the admirals orders exactly.
The main purpose of the Marines remain footed in the idea of bringing justice to any criminal. They use justice as their constituted policy to manage a world that is made entirely of one ocean much easier. However, the main problem within the Marines is the approach to Justice. They are generally divided between those who support Moral Justice and those who support Absolute Justice with the latter being the code of conduct for the Marines as a rule. Nevertheless, there is little worry from the higher ranked Marines as to how the Justice is carried out so long as it is, leading those who truly support absolute justice to make unjustified actions in carrying out their duties.
The Marines are also aided by the Shichibukai in terms of maintaining the "Three Great Powers", and as such, are expected to cooperate when necessary. Despite this, several Marines, such as Aokiji, Akainu, Smoker, Sengoku, and Kizaru think of the Shichibukai as no more than pirates. In turn, the Shichibukai have no obligations to obey the Marines unless under the direct orders of the World Government itself.
One of the most questionable parts of their "Justice" is when it comes to Slavery. Despite the practice supposedly being abolished years before, it is often shown that they just look the other way. Especially when it comes to the World Nobles' slaves, where it is even seen as a crime to free said slaves even if the person is merely a child. Often they are tasked to find and retrieve the person to be a slave once again.