http://www.xdcam-user.com/2014/05/what-is-a-gamut-or-color-space-and-why-do-i-need-to-know-about-it/

In video terms gamut is normally related to as the full range of colours and brightness that can be either captured or displayed.

Generally speaking all color gamuts recommendations are trying to define a reasonable level of color representation based on available technology and hardware. REC-601 represents the old TVs. REC-709 is currently the most distributed solution. P3 is mainly available in movie theaters and is now being adopted in some of the best new 4K HDR TVs. Rec2020 (a wider space than P3 that improves on visibke color representation) and ACES (the full coverage of visible color) are other common standards which see major hardware development these days.

To compare and visualize different solution (across video and printing solutions), most developers use the CIE color model chart as a reference.
The CIE color model is a color space model created by the International Commission on Illumination known as the Commission Internationale de l’Elcairage (CIE) in 1931. It is also known as the CIE XYZ color space or the CIE 1931 XYZ color space.
This chart represents the first defined quantitative link between distributions of wavelengths in the electromagnetic visible spectrum, and physiologically perceived colors in human color vision. Or basically, the range of color a typical human eye can perceive through visible light.

Note that while the human perception is quite wide, and generally speaking biased towards greens (we are apes after all), the amount of colors available through nature, generated through light reflection, tend to be a much smaller section. This is defined by the Pointer’s Chart.

In short. Color gamut is a representation of color coverage, used to describe data stored in images against available hardware and viewer technologies.

Camera color encoding from
https://www.slideshare.net/hpduiker/acescg-a-common-color-encoding-for-visual-effects-applications

CIE 1976

http://bernardsmith.eu/computatrum/scan_and_restore_archive_and_print/scanning/

https://store.yujiintl.com/blogs/high-cri-led/understanding-cie1931-and-cie-1976

The CIE 1931 standard has been replaced by a CIE 1976 standard. Below we can see the significance of this.

People have observed that the biggest issue with CIE 1931 is the lack of uniformity with chromaticity, the three dimension color space in rectangular coordinates is not visually uniformed.

The CIE 1976 (also called CIELUV) was created by the CIE in 1976. It was put forward in an attempt to provide a more uniform color spacing than CIE 1931 for colors at approximately the same luminance

The CIE 1976 standard colour space is more linear and variations in perceived colour between different people has also been reduced. The disproportionately large green-turquoise area in CIE 1931, which cannot be generated with existing computer screens, has been reduced.

If we move from CIE 1931 to the CIE 1976 standard colour space we can see that the improvements made in the gamut for the “new” iPad screen (as compared to the “old” iPad 2) are more evident in the CIE 1976 colour space than in the CIE 1931 colour space, particularly in the blues from aqua to deep blue.

https://dot-color.com/2012/08/14/color-space-confusion/

Despite its age, CIE 1931, named for the year of its adoption, remains a well-worn and familiar shorthand throughout the display industry. CIE 1931 is the primary language of customers. When a customer says that their current display “can do 72% of NTSC,” they implicitly mean 72% of NTSC 1953 color gamut as mapped against CIE 1931.

http://www.lightillusion.com/luts.html

https://www.shutterstock.com/blog/how-use-luts-color-grading

A LUT (Lookup Table) is essentially the modifier between two images, the original image and the displayed image, based on a mathematical formula. Basically conversion matrices of different complexities. There are different types of LUTS – viewing, transform, calibration, 1D and 3D.