The EU has been concerned for many years about the ability of multinationals to structure their companies in such a way that they pay as little tax as possible, shifting profits and costs between divisions in different countries.
It has accused some countries, such as Ireland, the Netherlands and Luxembourg, of helping companies avoid tax.
For example, the Commission believes Ireland gave illegal state aid to Apple.
Ireland's corporate tax rate is set at 12.5%, but Apple enjoys an effective tax rate of 2%, due to the way it channels overseas sales through its subsidiaries.
Apple has denied that it received any "selective treatment" while the Irish government has rebuffed claims that its actions breached EU rules.
Companies found guilty of breaching EU rules on state aid could be forced to repay what Brussels calculates as the amount of financial benefit they have received.