On Android devices, the affordable Chromecast is all you need to cast your screen to an external display. On iOS, that doesn't work. You need to buy a costly (and functionally crippled, IMO) Apple TV so mirror your screen.
A good alternative to that is to get a Lightning to HDMI adapter. You plug in your phone on one end, and HDMI out and USB Power Out on the other. It lets you mirror your display with no discernable latency.
Sadly this doesn't work for Netflix and other media streaming apps, though you can use Chromecast for that. Works great for what I wanted - to share pictures clicked with the camera onto a bigger screen. Worked fine with an iPhone 6, iPhone 7 Plus, iPhone X and iPad Air 1.