That really depends on Esri. If you're an SE customer, we're all frozen on version 10.2.1 at Esri's recommendation (FAQ: Our Support for Esri's Utility and Telecom Release of ArcGIS for Desktop)
Esri wants all the utility customers to get themselves to version 10.2.1 and stay there, only applying the Utility and Telecomm patches as they become available. They will let us and SE know when the next "utility" release of Arc is and it's not 10.3.1 nor is it even the latest release of ArcGIS. SE is working on the next generation of ArcFM (called the XI series) that will work with ArcGIS Pro and the new Utility Network, but that will not work with ArcGIS Desktop.
Just to clarify... David Miller's info is all correct if referring to ArcFM/ArcGIS Desktop. If its ArcFM Server then its a different matter.
For ArcFM Server the supported ArcGIS Server versions include the following: