An entity is a VIE when its equity is too small to finance itself without extra support, when equity holders lack control, or when their rights do not match their share of the risks and rewards. Typical examples are special-purpose entities, some joint ventures, financing vehicles and structures that hold a single asset.
For these, the usual test of who owns more than half of the voting shares does not decide who consolidates. Instead, the party that qualifies as the primary beneficiary consolidates. The rules were issued in 2003, as FIN 46(R), and now sit in ASC 810.
VIEs are also used in some foreign structures, such as for companies in China that list overseas, where the arrangement is built on contracts and not ownership.
Read the note on VIEs, compare the consolidated and unconsolidated ones and check what exposure the company has to the unconsolidated ones.