It depend what project version you are using Project 2000 or Project 2002 and try to open Project 2007 or Project 2010 than No converter is available. Ask the person who sent the Project 2007 or later file to save the file first in the Project 2000-2003 file format.
If you are using Project 2003 and trying to open Project 2007 than there may be two chances If you are using Project 2003 with SP3, project files from Project 2007 can be opened read-only. Or If you are using Project 2003 without SP3, there is no converter available. Upgrade to Project 2003 with SP3, or ask the person who sent the Project 2007 or later file to save the file first in the Project 2000-2003 file format.
And Project 2010, Project 2013, and Project 2016 all use the same file format. For example, a project created in Project 2016 can be opened in Project 2010 without saving the project to a different format.
And also for those who are using Project 2007 and they are trying to open Project 2010, Project 2013, or Project 2016 than No converter is available. If you received a Project 2010, Project 2013, or Project 2016 file that you want to open using Project 2007, ask the person who sent the file to first save it to the Project 2007 file format.