Which kind?
There is the hierarchical database ([https://en.wikipedia.org/wiki/Hierarchical_database_model](https://en.wikipedia.org/wiki/Hierarchical_database_model)) where data is organized into a tree structure. Very fast for certain kinds of searching, but not particularly popular anymore.
There is the navigational database ([https://en.wikipedia.org/wiki/Navigational_database](https://en.wikipedia.org/wiki/Navigational_database)), which a hierarchical is arguably a type of.
These were mostly popular when computers were still super expensive. But as relatively cheap disks and processors became available they were supplanted by the relational database.
Going forward, as computers continue to get faster, you now have object databases ([https://en.wikipedia.org/wiki/Object_database](https://en.wikipedia.org/wiki/Object_database)), NoSQL ([https://en.wikipedia.org/wiki/NoSQL](https://en.wikipedia.org/wiki/NoSQL)), and probably others as well.
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