Relational DataBase Management Systems (RDBMSs): working non-SQL implementations of the relational model.
About the original QUEL Ingres, which was relational.
Obsolete relational or quasi-relational implementations
This is reserved for quasi-relational implementations that are still somewhat better than the current state of the art -- meaning, at the moment, anything less in violation of the model than SQL.
Required Technologies holds some patents relevant to possible implementations of the relational model.
Rules Engines can be considered as implementations of the constraint aspect of the relational model.
Implementations striving for The Third Manifesto D compliance