LCD screens
Are almost universally made of plastics with multiple layers of soft surface film (up to 9 layers) that are vulnerable to salts and acids on hands and fingers (children) scratches, damage by sharp articles or improper cleaners.
Screen and computer manufacturers consistently warn against using alcohol or ammonia-based cleaners.
Repeated applications of alcohol based products on plastic will turn your screen surface yellow, make it brittle, and cause stress cracking (hairline scratches) on your screen surface. Also just water based cleaners (often with some citric acid) will damage your screen because of chalk and the acid content
Do not make the mistake of damaging your expensive screen using a cheap / inexpensive glass cleaner and a paper towel.
What is often the case is that the coatings work by creating a nano structure in the surface. This is effectively a very fine textured finish. What happens is that any type of residue (especially oil from fingers and hands) fills in this nano texture and is very difficult to remove from the bottom of the 'pits'. Therefore you can imagine that any houshold cleaner that may leave a residue of, say, silicone (to give a nice shine) will clog up the nano texture. This has the obvious visual effect but also destroys the antiglare property until it is removed.
CRT (cathode ray tube)
most of these monitors have amongst others, anti-glare coatings to help reduce reflections, they also often have coatings to enhance colours, brightness, clarity etc. and to protect the sensitive electronics. Salts and acids on hands/fingers (children!), scratches, damages by sharp articles or improper cleaners can easily damage these coatings.scratches and/or harsh cleaners can damage this surface.
Many large screen type TV's have a screen that is made of a plastic or acrylic type material. These type screens require special attention to clean properly and safely.
Plasma screens
are made of glass substrate but are usually coated for glare and radiation reduction.Glare reduction add-on screens are coated for reduced reflection. They also often have coatings to enhance colours, brightness, clarity etc. and to protect the sensitive electronics and radiation.
HDTV's
most have optical surface coatings for glare reduction, and color, brightness enhancement Optical coatings are often made of magnesium fluoride. There normally are multiple coatings (up to 9 layers) of this material, depending upon the degree of anti-reflectivity required.
The first generation of optical coatings was notorious for being very soft and very easy to scratch.
Recent coatings are "harder" and a bit more forgiving but are still relatively easy to scratch.
If the coating is scratched or damaged, it can't be repaired.