Sorry I'm a bit confused about SQL Server Data Tool (SSDT).

What I read on internet is this: "SQL Server Data Tools (SSDT) is a toolset which provides an integrated environment for database developers to carry out all their database design work for any SQL Server platform (both on and off premise) within Visual Studio. Database developers can use the SQL Server Object Explorer in VS to easily create or edit database objects and data, or execute queries."

But what is not clear to me is: if I haven't installed a SQL Server engine (e.g. SQL Server 2012), how to and where SSDT run/execute DDL/DML queries and store my .mdf file??

What I want ask to you is: Do SSDT is only a client tool or it provide also a server engine for run/execute DDL/DML queries and store my .mdf file??

thanks.