The streaming device plugs into your TV's HDMI port and connects to the internet via Wi-Fi. Other devices on the network, like your smartphone, can control the TV by interacting with compatible apps.
Miracast is a standard introduced by the Wi-Fi Alliance making it possible to stream your entire phone display. This is useful if you want to share more than a single media file or application.
Android users running later editions of the OS have Miracast. Many new TVs support Miracast, if yours doesn't, you can use an HDMI dongle to add the support.
It's also possible to control your TV from a mobile device using a Plex media server. We've covered how to set up Plex on the Raspberry Pi in the past. If you are using a Pi setup or desktop-based server, you can use the mobile app to control your current Plex playlist.
If you want to stream Plex content to your TV, you'll need something like Chromecast. You will need to be a Plex Premium member or purchase a one-time pass to use the mobile app with your server.
So you've got a fancy phone—way to go! No doubt that device in your pocket cost a pretty penny. It makes perfect sense that many of us want to keep our phones when we switch service providers.