The successor to the dynamic island on iPhone is apparently a true fullscreen display with zero bezels. This display will cover the screen from edge to edge and also feature an under-display camera system. However, Apple has been forced to postpone this evolution of the iPhone as the technology to make this display hasn't been perfected yet.
Similar displays have, of course, existed in the past. Samsung phones like the Galaxy S6 Edge Plus come to mind. But Apple isn't satisfied with how the displays were handled on those phones. As is tradition the company wants to do things the Apple way and that means an absolutely perfect display with no warped elements.
Both Samsung Display and LG Display are working on delivering this OLED panel to Apple. One of the persisting problems includes the warped effect you get on the sides after applying the optical clear adhesive. Reshaping internal circuitry as well as accounting for the increased fragility of such a display are also problems under consideration.