Verizon pre-announced its VoLTE service a few weeks ago, but now it's rolling out. Customers can finally start taking advantage of VoLTE calling starting today—that assumes people still make phone calls, which is debatable. You need to have a supported device of course, and there are still a few caveats.
AT&T has announced that the Galaxy S4 Mini, yes - the phone that came out back in November, is coming to the carrier May 23rd with HD Voice. It will be the first device on the network with support for making VoLTE (voice over LTE) calls. The handset isn't available for pre-order, but the carrier does have it listed as "coming soon."
AT&T is the first carrier to support making voice calls over LTE, supporting simultaneous voice and data over the IP network.