Prime Minister David Cameron's demand for key reforms in return for Britain's continued membership has exposed a rift over whether the EU's future is to move ever closer together or to ease ties, becoming a looser group of distinct sovereign nations.
Fail to get a deal and Cameron has said anything is possible, including Britain becoming the first country to leave the 28-nation bloc after an in-or-out referendum that could come as early as this summer.
Leaders will also seek to get a new grip on the refugee crisis, which has seen over a million migrants flood into Europe.
Most of them are Syrians making their way from Turkey via Greece, which has been overwhelmed by the numbers.
Brussels has rounded on Athens, saying it is not doing enough, but a solution is elusive. Some member states are taking measures unilaterally, such as re-imposing border controls in the passport-free Schengen zone to halt an apparently unending tide of humanity.