We have been expecting it since vSphere 4.1; VMware announced on Wed 18th May 2016 that the current version of vSphere, 6.0, will be the last version to contain the C# Client, i.e. the full desktop client we have been using since vSphere 4 and before the Web Client was available.
The Web Client that has been available since vSphere 5 has had issues with performance with many people resisting the move to it, preferring the C# desktop client even though the web client has been improved over the various releases through 5.5 and 6.0. VMware stopped adding new features to the traditional C# client with 5.5 meaning that we had to use the Web Client to utilise these new features, such as Inventory Tags, enhanced vMotion (no shared storage), vSphere Flash Read Cache and VMDKs over 2TB. This Web Client was based on Flash; a new web client based on HTML5 has recently been made available via a VMware Fling. A VMware Fling is an unsupported release which allows VMware to get features out to customer early for testing. It is this HTML5 based web client that will be included in the next version of vSphere.
The VMware Fling HTML5 Web Client is not a fully functional client at the moment but I would encourage people using vSphere 6 to download it now and start using it so that they can get used to it and try it out prior to it being the main client available. VMware Flings also allow VMware to release updates much more quickly than official supported code, therefore expect new features to be added to this client over the coming weeks and months.
The HTML5 Web Client VMware Fling can be downloaded from https://labs.vmware.com/flings/vsphere-html5-web-client
For more details on the announcement from VMware regarding the vSphere C# Client not being included in the next release of vSphere see http://blogs.vmware.com/vsphere/2016/05/goodbye-vsphere-client-for-windows-c-hello-html5.html