The Legal Entity Identifier(LEI) initiative was created as part of the G20 requirements to reduce systemic risk, so that legal entities will have a common and traceable identifier on reports, allowing regulators to track exposures. This page on the GLEIF website explains the process further.
MiFID II requires that all transaction reports, in all asset classes, use LEIs to identify parties to a trade. The requirement follows the push under EMIR to use LEIs for all derivatives reporting. This article on DerivSource by Ron Jordan looks at the growing number of registrations of LEIs because of MiFID II. it also outlines the requirement to now provide parent level information on records as well. There is also mention of the issue of some entities not renewing their LEI registration which is now being addressed by regulators globally.
This article by Shanny Basar on Markets Media also looks at the issues, the likely surge in registrations in Q4, and the lack of registrations in Asia.