Curved screen
A curved screen is an electronic display device that, contrasting with the flat-panel display, features a concave viewing surface. Curved screen TVs were introduced to the consumer market in 2013, primarily due to the efforts of Korean companies Samsung and LG, while curved screen projection displays, such as the Cinerama, have existed since the 1950s.

Analysis
Curved screens are often marketed as being able to 
provide an "immersive" experience, and allowing a wider field of view.    However, the field of view (FoV) is the extent of the observable world that is seen.

This type of screen is an optical instrument with a solid angle through which we can see what's happening inside the "computer world". If a screen is curved, the FoV of a person who looks at a picture on screen would not change. Most curved screens are made with wide (16:9), ultra-wide (21:9 / 64:27) or super ultra-wide (32:9 or 18:5) aspect ratio. Wider screens provide a wider angle of view, field of view.

Field of view calculations are the reason wider screens are able to display more information on this type of screen, not curvature in and of itself.

The optimal position of viewing a screen is directly along the central axis of the TV with the central point of the screen at eye level. Other viewing positions or angles may cause degradations in picture quality ranging anywhere from minor to severe, the most notable being trapezoidal distortion.

Manufacturers suggest that curved screens allow greater range in satisfactory viewing angles and offer minimal trapezoidal distortion in comparison to flat-screens. This claim is heavily disputed by another claim that a substantial offset from the center provides greater viewing distortion than that of a flat screen. However, the equidistant claim by manufacturers of the various parts of the screen from a centered view is supported. 

Additionally, curved TVs supposedly offer minimized glare from ambient light.

Applications
To reduce outer edge distortions and provide a panoramic view, large curved screens accomplish this free of bezel lines framing each screen, and the alternative was to use multiple flat-screen monitors around the viewer. Curved screens and multi-screens have applications in gaming.

Backward curved screens have the potential to be used as digital signage that can be installed at various locations to produce marketing exposure.

Projection screens
When projecting images onto a completely flat screen, the distance light has to travel from its point of origin (i.e., the projector) increases the farther away the destination point is from the screen's center. This variance in the distance traveled results in a distortion phenomenon known as the pincushion effect, where the image at the left and right edges of the screen becomes bowed inwards and stretched vertically, making the entire image appear blurry.

Curved screens are also widely used in IMAX and standard movie theaters for their ability to produce natural expressions and draw the audience deeper into the scene.

Touch on curved screen
One of the issues in the use of the curved screen in commercial electronics is how accurately it can work with a touch-sensor. To drive the solution, LG electronics has developed Infrared-based touch solutions for the curved display.

History
The first curved screen was the Cinerama, which debuted in New York in 1952. Multiple theaters, including the Cinerama Dome in Hollywood began to use horizontally curved screens to counter image distortions associated with super-wide formats such as 23:9 CinemaScope.

21:9 aspect ratio monitors were developed in order to display the maximum amount of information on a single screen. However, the extreme wideness of the screen created severe distortions on the left and right edges of the screen. Curved 21:9 monitors were then developed to address this issue and provide a distortion-free, wide-angle viewing environment.

Manufacturing process
The first curved panels were produced by bending flat panels that had already been manufactured. This technique resulted in performance issues, such as oval mura (clouding effect) and color mixture (which causes color impurity and image distortion) observed at its curved edges.
Since the introduction of flexible glass, liquid crystal displays (LCDs) can be applied to curved surfaces without bending existing panels.
The screen technologies used to create curved LCD screens are Vertical Alignment, which helps to reduce any white glow that may affect an angular view, and IPS Panels, which are more susceptible to distortion.

See also 

 MSG Sphere
 IMAX Dome
Evans & Sutherland

References

Television technology
Display technology