The Razor templating engine is a versatile tool that allows developers to mix raw output with programmatic statements in their ASP.NET Core views, providing features like partial views, layouts, tag helpers, and more. It's designed specifically for use with C# and other .NET code, but its underlying technology can be used by other languages and frameworks as well. The Razor engine processes templates in four phases: parsing, code generation, compilation, and execution, which involve separating code from content, converting the template into C# code, compiling it into an assembly, and executing the render method to produce final content. While Razor is often associated with ASP.NET Core, its underlying engine can be used by other frameworks and libraries, making it a flexible and extensible tool for developers.