The Internet Archive Wayback Machine is fully compliant with the Memento Protocol. The Memento API provides additional interfaces for querying snapshots (e.g. Mementos) in the Wayback Machine. The Availability API is partially based on the Memento APIs.

Browse examples of Memento support in the Wayback Machine

Wayback CDX Server API
The CDX Server is another API which allows for complex querying, filtering and analysis of Wayback capture data. If you are looking for more in depth information about Wayback machine data, please take a look at the CDX server API.

The latest documentation on the CDX server can be found at: Wayback CDX Server @ GitHub