Battlefield 3 and 4's servers are still running and are very much active. There's more optimal ways of playing these games but it's so cool to be able to still play them
Battlefield 3 Servers on the Xbox 360 is Down; no ETA yet [Update] - Just Push Start
Battlefield 3: Console Custom Servers Features Trailer - YouTube
PS3 & XBOX Battlefield 3 Server Browser Guide - Lzuruha Forums
Massive Battlefield 3 Patch And Dedicated Servers Arriving On PS3 Consoles Tomorrow