How is the marked up data processed? How soon is it displayed in the search results?

Microformat markup is processed at the same time when your site is indexed by the Yandex search robot. Sites are crawled at different speeds. It usually depends on how often the site is updated. For more information about the indexing process, read theSite indexing help section.

For hCard, we recommend to add URLs of marked up pages in the sitemap file to tell the robot that this page is important.

The data extracted from the markup is moderated or automatically checked before it is added to the search. The check duration can depend on the data type.

How safe is using semantic markup?

Microformats are fully open formats. This means that you can't control which services extract the data and how they use it. However, any publicly available information may be used by hackers. Semantic markup just facilitates extracting data from the page body. Avoiding it doesn't guarantee security.

In any case, it is up to you which microformats to use and which data exactly to mark up.