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
Amazon.com: Electronic Arts Battlefield 3 - Limited Edition (Ps3) : Video Games
Battlefield 3 docs reveal server options, filters, 64p maximum on all modes - Neoseeker
'Battlefield 3' servers quadrupled by DICE - Polygon
Battlefield 3: How Fan-Run Servers Are Ruining DICE's Game | Eurogamer.net
Battlefield 3 mod allows unofficial dedicated servers, more | VG247