There are some recent announcements for Visio that are exciting.
First, Visio Online has been released in Preview and you have the ability to add it to your tenant through the Office 365 First Release program. This feature allows you to view Visio diagrams through a browser. For the preview it currently only allows you to view Visio diagrams.
This capability is different from the traditional Visio Services that is part of SharePoint Online Plan 2 (which is part of E3). Visio Services I would term as the legacy solution from SharePoint Enterprise to allow you to render Visio diagrams through browser. This new Visio Services capability is the solution moving forward and is aligned with Office Online.
Visio on iPad
Second, a preview of Visio on iPad App has been released. This allows you have a nice Visio app to access your drawings stored in OneDrive for Business, SharePoint Online, etc.
Public Announcement - https://blogs.office.com/2016/08/31/visio-updates-advanced-design-collaboration-data-linked-diagrams-and-cross-platform-coverage/
Visio Online Preview - https://products.office.com/en-us/visio/visio-online
Visio Online FAQs for Preview - https://support.office.com/en-us/article/Visio-Online-Frequently-Asked-Questions-e6647040-2fca-42ec-9fa5-d16a4e39e0ee
Visio for iPad Insider Program - https://products.office.com/en-us/visio/visio-for-ipad
Visio for iPad Insider Program FAQs - https://support.office.com/en-us/article/Visio-on-iPad-Insider-Program-3dc2390d-6192-4fed-8b07-0647da2ccf3e