Microsoft confirms Remote Desktop app is coming to Windows Phone
It seems like even Microsoft is prioritizing the more successful mobile platforms over its own Windows Phone OS with this one, although that isn't Microsoft's excuse. According to a spokesperson for Microsoft, the reason why there is no Windows Phone app is because "Remote desktop on phones is a relatively rare usage scenario." This (partially) explains why there is a Windows RT app, but no Windows Phone app. However, this is a good time to reiterate that the app released on Thursday does work on iPhones and Android smartphones.
Microsoft confirmed that there is a Remote Desktop app in the works for Windows Phone, but could not speak to a timetable for that app's release. If you're a Windows Phone user, there is an official option on the way, but you can always use an alternative that's already in the Windows Phone Store.
source: The Next Web