Could not load file or assembly 'System.Web.Http.WebHost, Version=4.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35' or one of its dependencies. The system cannot find the file specified.

If you are getting the next error when deploying your web application:

Could not load file or assembly 'System.Web.Http.WebHost, Version=4.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35' or one of its dependencies. The system cannot find the file specified.

or the next error:

Could not load file or assembly 'System.Web.Http.WebHost, Version=4.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35' or one of its dependencies. The system cannot find the file specified.

or this one:

Could not load file or assembly 'System.Net.Http.Formatting, Version=4.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35' or one of its dependencies. The system cannot find the file specified.

Or maybe other files, the reason is the .dll is missing in the published site.
To solve the problem in visual studio:

• Expand the References folder
• Click on the file missing
• On the properties section go to the Copy Local option
• Change the value from False to True

This should fix the problem.