VoLTE has become a pretty popular topic as of late, especially when it comes to wireless networks, as it's the next logical step for calls. Currently, phone calls are made over a legacy voice network, which wireless operators want their users to do this over LTE, because LTE gives them more bandwidth for both data and voice. On top of that, doing calls over VoLTE means they can refarm the spectrum used for their legacy voice network. This also means that users can have higher-quality calls by using VoLTE. However, with VoLTE, each carrier is implementing it differently. And currently, none of the US carriers have it available nationwide. Which means you can't use T-Mobile to call a Verizon user over VoLTE. But that may change in the near future, thanks to interoperable VoLTE.
AT&T has confirmed that they have rolled out interoperable VoLTE to some of their users. When these users call select Verizon users, they will be able to do so over LTE (which is a change that the network does, the user needs to do absolutely nothing here). AT&T said in a statement that they are "working with Verizon to allow our customers to enjoy clear audio quality and video calling features when placing VoLTE calls to Verizon customers and vice versa." AT&T also noted that "in December, we saw the first VoLTE exchange between our customers and Verizon's in limited, select areas. We're working with others on this same feature, too." Meaning that it shouldn't be long before AT&T customers can call those on Sprint, T-Mobile and other networks over LTE, and vice versa.
A few users over on Reddit have also noted that they have been seeing interoperable HD voice over VoLTE in some markets. Unfortunately, it's not available across the country, but it is available in a few markets. Which is definitely better than nothing. It's likely that both AT&T and Verizon are still testing out interoperable VoLTE to see how well it works and if anything needs to be tweaked before they roll it out to their entire user base.
If you've made a call over LTE recently, then you probably noticed a difference in the call quality - not to mention that with LTE, you are less likely to experience dropped calls. This is something that is going to become more and more popular over the next few years as the carriers move more and more to LTE for voice calls and video calls.