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The answer is short: the ADO & ODBC tandem.
ADO is a programming interface to access data in a database. As from IIS 4 (Windows 98, PWS), the ADO programming interface ships with IIS as a built-in interface. ODBC stands for Open Database Connectivity. ODBC is a standard application programming interface (API) for accessing database management systems (DBMS). It's available to any Windows operating system as from Windows 95. (source: Wikipedia)
Long story short: in classic ASP - when using the the IIS-built-in ADObjects - you can connect to any popular DBMS (Access, Oracle, MySQL, SQL Server, PostgreSQL, ...) by simply creating an ODBC connection on your local computer or server.
To use such DSN in your classic ASP application:
dim db : det db = Server.Createobject("ADODB.Connection")
db.Open "DSN=mySQL" (in case you named your ODBC connection "mySQL")
From there on, your can launch any CRUD (Create, Read, Update, Delete) statement against your data. Both MySQL, SQL Server, Oracle and PostgreSQL provide 64bit ODBC drivers. So classic ASP developers benefit from the very latest bug fixes and improvements that come with every new release of any given ODBC driver.
This is amazing. And it somehow ensures that classic ASP is there to stay. Even if it's going nowhere. Perhaps ... because it's going nowhere. I really think so.