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There are several competing DVD Formats:
Non-recordable formats 
- DVD-ROM: These are pressed similarly to CDs. The reflective surface is silver or gold colored. They can be single-sided/single-layered, single-sided/double-layered, double-sided/single-layered, or double-sided/double-layered. As of 2004, new double-sided discs have become increasingly rare.
- DVD-D: Self-destructing disposable DVD format introduced in 2008. Like EZ-D, it is sold in an airtight package, and begins to destroy itself by oxidation after several hours.
- DVD Plus: combines both DVD and CD technologies by providing the CD layer and a DVD layer. Not to be confused with the DVD+ formats below.
- DVD-R for Authoring: a special-purpose DVD-R used to record DVD masters, which can then be duplicated to pressed DVDs by a duplication plant. They require a special DVD-R recorder, and are not often used nowadays since many duplicators can now accept ordinary DVD-R masters.
- DVD-R (strictly DVD-R for General): can record up to 4.7 GB in a similar fashion to a CD-R disc. Once recorded and finalized it can be played by most DVD-ROM players.
- DVD-RW: can record up to 4.7 GB in a similar fashion to a CD-RW disc.
- DVD-R DL: a derivative of DVD-R that uses double-layer recordable discs to store up to 8.5 GB of data.
- DVD-RW DL: a derivative of DVD-RW that uses double-layer recordable discs to store up to 8.5 GB of data.
- DVD-RAM (current specification is version 2.1): 2.6 GB, 4.7 GB or 9.4 GB (double-sided) discs compatible with only a small proportion of other-format DVD drives. DVD-RAM discs were originally typically housed in a cartridge, though these are now less commonly required. Discs can be removed from their caddy and used in compatible standard-tray drives. Rewritable many more times than other rewritable formats.
- DVD-AR: Recordable version of DVD-Audio
Recordable formats, supported by the DVD+RW Alliance 
- DVD+R: can record up to 4.7 GB single-layered/single-sided DVD+R disc, at up to 16× speed. As with DVD-R it can only be recorded on once.
- DVD+RW: can record up to 4.7 GB at up to 16× speed. Since it is rewritable it can be overwritten several times. It does not need special "pre-pits" or finalization to be played in a DVD player.
- DVD+R DL: a derivate of DVD+R that uses dual-layer recordable discs to store up to 8.5 GB of data.
- DVD+RW DL: a derivate of DVD+RW that uses dual-layer recordable discs to store up to 8.5 GB of data.
Recordable format compatibility 
DVD drives from 2004 should be able to read either of the competing recordable formats, older drives may favour DVD-R discs. Modern drives (certainly at time of writing in 2007) typically allow writing to both DVD-R[W] and DVD+R[W] discs making the difference largely irrelevant to the average consumer.
Application formats 
|This section may need to be rewritten entirely to comply with Wikipedia's quality standards. (May 2009)|
VR Mode (aka Video Recording): This is a new format that allows editing/deleting titles and getting the total of space of deleted titles back/recording of copy once broadcasts/defect management. Used by DVD-RAM (DVD-RAM only uses this format) and DVD-RW. Because it is a newer format than DVD Video, it will only playback in modern DVD Players that support it.
Video mode This is the standard DVD Video mode format, the same format DVD films come in. Because the DVD Video format was invented before DVDs were recordable it doesn't allow editing on the disc, doesn't support defect management (so not as robust for continuous everyday recording and wiping), if you delete a title you may not get the space back without completely erasing the disc, and needs a finalise step to play elsewhere. As it is the same format as commercial DVD films, it is normal for it to work in most DVD Players. Can be used on DVD-RW and DVD-R discs, never used DVD-RAM. Most (but not all) recorders that use DVD-RW will give you choice of VR mode or Video mode.
+VR Introduced by Philips for use on DVD+RW. The idea was to keep compatibility with the DVD Video format so it could be played elsewhere, but try and introduce some features as found in the VR mode used on DVD-RW/DVD-RAM. DVD+RW normally always uses this mode in set-top recorders. It doesn't need a separate finalise step to play in other DVD recorders; finalisation is just done in the background, which makes it bit easier to use (i.e. you can't forget to do it), but it does put extra wear on the disc, as the same area of the disc is updated every time it is used. Due to DVD-Video not being able to take advantage of defect management and the extra overheads of background finalising after each edit or recording, the +VR mode has always been the least reliable, and the editing features may be missing on some DVD recorders to make it more robust.
Because Video Mode and VR mode are Forum standards, they are only used when recording to DVD approved formats i.e. DVD-RAM/DVD-RW/DVD-R discs. DVD+RW isn't approved by the DVD Forum so can't get a license to use the above modes, hence Philips introducing their own +VR mode, so DVD+RW gets +VR and generally they are not mixed.
However, many cheaper recorders are mixing these formats up now and typically this means not bothering to get the recorder approved by the DVD verification labs and so not paying the appropriate licence fee or reaching a certain level of quality or compatibility, and so just use +VR mode on DVD-RW and DVD+RW. You can tell these by the lack of the DVD-Video logo.
+VR mode error: copy protection shown when attempting to copy a program that has been copy protected, and the unit records in +VR mode.