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Envy-free item allocation is a fair item allocation problem, in which the fairness criterion is envy-freeness - each agent should receive a bundle that they believe to be at least as good as the bundle of any other agent.
Since the items are indivisible, an EF assignment may not exist. The simplest case is when there is a single item and at least two agents: if the item is assigned to one agent, the other will envy.
One way to attain fairness is to use monetary transfers; see Fair allocation of items and money. When monetary transfers are not allowed or not desired, there are allocation algorithms providing various kinds of relaxations.