The first major battle is likely to be about money. The EU says Britain must pay a hefty divorce bill of up to 60 billion euros ($64 billion), to cover EU staff pensions and other expenses the U.K. has committed to. Britain hasn't ruled out a payment, but is sure to quibble over the size of the tab.
There's also likely to be friction over Britain's desire to maintain free trade in goods and services with the bloc, without accepting the EU's core principle of free movement of workers. Britain has said it will impose limits on immigration, and so will have to leave the EU's single market and customs union. That makes some barriers to trade seem inevitable.