It should be possible to just simply re-save (File ► Save as..) VSD files to VSDX format in the latest version of Microsoft Visio, you cannot possibly do that using much older versions of the program, because it was introduced in office 2010 or so.
Except for Visio, some third party alternatives might also be capable of vsd to vsdx conversion, but considering Visio format is somewhat closed, not every program might support the latest version of Visio formatsOpen VSD file Open VSDX file
Graphic and diagram software from LibreOffice suite
Powerful multimedia presentation software tool from LibreOffice suite
A vector based diagramming software from Microsoft