The primary software that lets you open a DOCX file is Microsoft Word 2007 (and above). If you are using an earlier version of Microsoft Word, you can download the free Microsoft Office Compatibility Pack which would allow you to open, edit and save DOCX files in your older version of MS Word.
For those who do not have Microsoft Word at all, there is a free programme available called Word Viewer, through which you can open DOCX files, without having to purchase the MS Office.
If for any reason, you decide to stay away from Microsoft products altogether, there are other readers that are compatible with DOCX files. These include WPS, OpenOffice Writer, ONLYOFFICE or Google Docs. Those are all free and allow you to open and edit the files.
For Apple product users, DOCX files can be opened using the built-in application called Pages.