Here is a quick answer to a common question about file format compatibility with Visio Services.
In Visio 2013 you can choose to save in a number of different file formats:
This is the new file format for 2013 and is also the new default file format. This format is compatible with Visio Services 2013 only. While you can save a VSDX file to SharePoint 2010, Visio Services will not be able to render it in the browser.
This format was introduced in Visio 2010 and is the format that is rendered by Visio Services in SharePoint 2010. In Visio 2013 you can still open and save using the VDW file format, allowing you to save diagrams that can be rendered by Visio Services in SharePoint 2010.
Visio Service in SharePoint 2013 can render both VSDX and VDW file formats.
You can still open and save using the VSD file format with Visio 2013, most likely when you need to work on older drawings or others in your organization have not upgraded to Visio 2013 yet. While you can save a VSD file to SharePoint, VSD is not compatible with any version of Visio Services.