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The first form of digital Optical Disc, and one of the two most popular and ubiquitous forms (the other being DVDs). Compact Discs, or CDs as they are generally known, are usually 12 centimetres (approx. 5") across and are shiny on at least one side (the one without a label painted or burned on). They are mostly used for two things: music and computer data. (Yes, all those free coasters from your favorite ISP were compact discs, and the ones on sale for ten bucks at the checkout counter still are.) The two can overlap - MP 3 CDs are gaining popularity. They're "compact" because they're smaller than phonograph records.
In its original form, the format can hold up to 650 megabytes of data or 74 minutes of "CD Quality" music (the number was supposedly chosen because a Sony executive figured that that was just long enough to hold all of Ludwig Van Beethoven's Ninth Symphony). Unofficial revisions pushed this limit up to 870 megabytes of data or 99 minutes of audio. Data CDs these days usually hold 700 megabytes. Music CDs are about the same as they ever have been, since the record labels rarely use all 74 minutes. Not every CD a record label releases is a music CD, however; if it also contains music videos, then it's a data CD. That kind may be marked "enhanced".
CD drives use a simple multiplier to indicate how fast they could read data. The base specification, 1x (150 kbps), is the minimum speed required to play CD quality music. CD players and drives are usually stamped with the maximum speed they are rated for; the higher the speed, the faster they can record (if the player is built for it), and the faster a computer can read data off them.
Almost all drives that can hold a disc the size and shape of a normal CD can play a normal audio CD. Many of them also play data CDs; the popularity of the MP3 CD and the enhanced CD has killed some forms of CD Copy Protection.
The standard for CDs declares only a maximum size. Undersized and oddly shaped CDs did and still do fly around. Early on, there were hopes that the 8cm (approx. 3") audio CD would make a good single format, but 8cm CDs didn't fit well in normal 12cm CD players, and slot-loaders won't unload 8cm CDs. There are structural requirements when you spin a disc at thousands of revolutions per minute, but heart-shaped and square CDs are sturdy enough for novelty stores. Business card-sized CDs are still popular in some technical circles, especially for groups that provide electronic media. Slot loaders won't unload them, either, but most computer CD drives aren't slot-loaders.
CDs remain the most popular choice for music and smaller installation programs, although these years the internet has started to be a serious contender for the role in data storage and transmission. Nearly every console with 32 bits or more uses CDs for some or all of its games. The Sega Dreamcast used a custom one-gigabyte version of the CD-ROM called the "GD-ROM" format instead of CDs or DVDs as a cost-saving and anti-piracy measure - which would have worked better if their GD-ROM player didn't also play normal data CDs (often, the GD-ROM contents minus copy protection pieces would fit on a CD-ROM.)
Incidentally, the CD's odd sample rate (44.1 kHz, which is tough to convert from since it's not an even multiple of 8000 like most other formats) was chosen because it matches well with both NTSC and PAL monochrome video carriers. This is because early digital audio work used a VCR with a device called a "PCM adapter" attached for data transfer. Back in 1980, when the CD-DA format was being worked on, multi-megabyte hard drives were still very much the realm of data centers, and tape provided the needed capacity in a package that was far less expensive and more portable. The video tape connection is also why CDs give their block addresses in minutes, seconds and frames -- it's carried over from the SMPTE time code used on U-matic tapes, though running at 75 frames per second instead of the normal 25 or 30.
A standard for Video Compact Disc, or VCD, also exists. Both video quality and program length (about an hour) are less than with DVDs, though DVD players and many CD-based game consoles are capable of playing them. VCDs never really caught on in the Western world, where most people stayed with VHS until DVDs came along, but became very popular in some Asian countries.