Citrix is by many perceived to own the most comprehensive portfolio for desktop virtualization alongside with the largest overall market share.
Citrixs success in this space is historically based on its Terminal Services-like capabilities (Hosted SHARED Desktops i.e. XenApp aka Presentation Server) but Citrix has over time added VDI (Hosted Virtual Desktops), mobility management (XenMobile), networking (NetScaler), cloud for Service Providers hosting desktop/apps (CloudPlatform) and other comprehensive capabilities to its portfolio (separate fee-based offerings).

Citrixs FlexCast approach promotes the any type of virtual desktop to any device philosophy and facilitates the use of different delivery technologies (e.g. VDI, application publishing or streaming, client hypervisor etc.) depending on the respective use case (so not a one fits all approach).

XenDesktop 7.x history:
- Citrixs announcement of Project Avalon in 2011 promised the integration of a unified desktop / application virtualization capability into its CloudPlatform product. This was then broken up into the Excalibur Project (unifying XenDesktop and XenApp in the XenDesktop 7.x product) and the Merlin Release aiming to provide multi-tenant clouds to manage virtual desktops and applications.

- XenDesktop 7.1 added support for Windows Server 2012 R2 and Windows 8.1, and new Studio configuration of server-based graphical processing units (GPUs) considered an essential hardware component for supporting virtualized delivery of 3D professional graphics applications.

- In Jan 2014 Citrix announced that XenApp is back as product name, rather than using XenDesktop to refer to VDI as well as desktop/application publishing capabilities, also see http://gtnr.it/14KYg4b

- With XenDesktop 7.5 Citrix announced the capability to provision application and or desktop workloads to public and or private cloud infrastructures (Citrix CloudPlatform, Amazon and (later) Windows Azure. Wake-on-LAN capability has been added to Remote PC Access and AppDNA is now included in the product.

-With XenDesktop 7.6 includes new features like: session prelaunch and session linger; support for unauthenticated (anonymous) users and connection leasing makes recently used applications and desktops available even when the Site database in unavailable.

VDI in a Box: Citrix also has VDI in a Box (ViaB) offering (originating in the Kaviza acquisition) - a simple to deploy, easy to manage and scale VDI solution targeting smaller deployments and limited use cases.
In reality ViaB box scales to larger (thousaunds of users) environments but has (due to its simplified nature and product positioning) restricted use cases compared to the full XenDesktop (There is no direct migration path between ViaB and XenDesktop). ViaB can for instance not provide advanced Hosted Shared Desktops (VDI only), no advanced graphics capabilities (HDX3DPro), has limited HA for fully persistent desktops, no inherent multi-site management capabilities.
Overview here: http://bit.ly/1fXeA38

Recommended Read for VDI Comparison (Ruben Spruijts VDI Smackdown): http://www.pqr.com/downloadformulier?file=VDI_Smackdown.pdf