TeX Live 2021 is available for download now. It is also available on DVD from TUG and other user groups.
You can acquire TeX Live in many ways. For typical use, we recommend the first two:
The last general update of packages and programs for the DVD was made around 24 March 2021. However, we continuously update packages in TL as they are released to CTAN. Post-installation updates are done with the tlmgr program. tlmgr also provides many other TeX installation options and features, explained in the tlmgr documentation.
Although it is possible to update continuously, it is not necessary or particularly recommended. The set of packages and programs that were included in the official release will most likely suffice unless you know that you specifically need updates made since then. That set is also the only one which gets tested as a coherent release. On the other hand, if you like to get updates as they happen, please report problems you find to the package authors.
Older releases of TeX Live are available under systems/texlive/ in the historic archive; both the initial release each year (that's on the DVD release), and the frozen state at the end of the cycle in tlnet-final/ subdirectory. You might find one useful if you need a release of particular vintage. The installation archives are in the same places.
There's no problem with having multiple versions of TL installed (in different directories); in fact, the default directory structure is arranged to facilitate this. After installation, just set your PATH accordingly.
If you have an older release installed, and want to update or install a given package, this can be done using one of the above directories as the repository. For example, to get a package as it was at the end of the 2019 cycle:
tlmgr option repository http://ftp.math.utah.edu/pub/tex/historic/systems/texlive/2019/tlnet-final tlmgr update ...
The historic repository has several mirrors (more mirrors are welcome), so please choose the best one for you.
This page is about acquiring the “original” TeX Live—the version of TeX released by the TeX user groups. If you want to get TeX as it is packaged by the myriad operating system distros, see the information available from the particular distro you want. Some distro links.