Question: More and more [`tar`](http://www.gnu.org/software/tar/manual/tar.html) archives use the [`xz`](http://en.wikipedia.org/wiki/Xz) format based on LZMA2 for compression instead of the traditional [`bzip2(bz2)`](http://en.wikipedia.org/wiki/Bz2) compression. In fact *kernel.org* made a late "*Good-bye bzip2*" [announcement, 27th Dec. 2013](https://www.kernel.org/happy-new-year-and-good-bye-bzip2.html), indicating kernel sources would from this point on be released in both tar.gz and tar.xz format - and on the main page of the [website](https://www.kernel.org/) what's directly offered is in `tar.xz`.

Are there any specific reasons explaining why this is happening and what is the relevance of [`gzip`](http://en.wikipedia.org/wiki/Gzip) in this context?

Answer: 
First of all, this question is not directly related to `tar`. Tar just creates an uncompressed archive, the compression is then applied later on.

Gzip is known to be relatively fast when compared to LZMA2 and bzip2. If speed matters, `gzip` (especially the multithreaded implementation [`pigz`](http://zlib.net/pigz/)) is often a good compromise between compression speed and compression ratio. Although there are alternatives if speed is an issue (e.g. LZ4).

However, if a high compression ratio is desired LZMA2 beats `bzip2` in almost every aspect. The compression speed is often slower, but it decompresses much faster and provides a much better compression ratio at the cost of higher memory usage.

There is not much reason to use `bzip2` any more, except of backwards compatibility. Furthermore, LZMA2 was desiged with multithreading in mind and many implementations by default make use of multicore CPUs (unfortunately `xz` on Linux does not do this, yet). This makes sense since the clock speeds won't increase any more but the number of cores will.

There are multithreaded `bzip2` implementations (e.g. [`pbzip`](http://compression.ca/pbzip2/)), but they are often not installed by default. Also note that multithreaded `bzip2` only really pay off while *compressing* whereas decompression uses a single thread if the file was compress using a single threaded `bzip2`, in contrast to LZMA2. Parallel `bzip2` variants can only leverage multicore CPUs if the file was compressed using a parallel `bzip2` version, which is often not the case.
**Short answer** : xz is more efficient in terms of compression ratio. So it saves disk space and optimizes the transfer through the network.  

You can see this [Quick Benchmark](http://catchchallenger.first-world.info/wiki/Quick_Benchmark:_Gzip_vs_Bzip2_vs_LZMA_vs_XZ_vs_LZ4_vs_LZO) so as to discover the difference by practical tests.