USB Type-C is fast becoming the standard for mobile devices, and it's more than just a reversible plug design. USB Type-C can do a lot more than microUSB could, and that now includes native HDMI output. The HDMI Founders organization has developed HDMI Alternate Mode for Type-C, which could enable easy video-out on future devices.
This is an alternate mode for USB Type-C similar to the existing audio and DisplayPort modes. HDMI support could be a big deal simply because HDMI is so common. Every TV sold in the last decade has at least a few HDMI ports. HDMI Alt Mode will support all the features of HDMI 1.4b including 4K video, surround sound, HDMI ethernet, HDCP, and more. It's passive, so the cable should be cheap and light weight.
It will be up to device makers to integrate HDMI Alt Mode, so nothing available at the moment has support for it. This won't just be for phones, either. Anything with a Type-C port would support HDMI Alt Mode including computers, tablets, and so on. The specification is available to all active HDMI Adopters.