TeX Live 2021 was released on April 1.
For typical needs, we recommend starting the TeX Live installation by downloading install-tl-windows.exe for Windows (~20mb), or install-tl-unx.tar.gz (~5mb) for everything else. There is also a zip archive install-tl.zip (~25mb) which is the same as the .exe. Although the .zip archive works fine on all platforms, the .tar.gz is much smaller, since it omits installation support programs needed only on Windows. The archives are otherwise identical.
The above links use the generic mirror.ctan.org url which autoredirects to a CTAN mirror that should be reasonably nearby and reasonably up to date. However, perfect synchronization is not possible; if you have troubles following the links, your best bet is to replace the mirror.ctan.org in the above urls with a specific host from the list of CTAN mirrors.
After unpacking the archive, change to the resulting install-tl-* subdirectory. Then follow the quick installation instructions or read the documentation.
For regular installations via download, we highly recommend installing the LWP Perl bundle if you don't have it (check for a file named LWP/UserAgent.pm). Any reasonable version of LWP available either from your operating system distribution or from CPAN should be fine for TL. Having it will greatly speed the downloads, over using the fallback curl or wget programs. On Windows, the TL-provided Perl already includes it, so nothing extra need be done.
If you need to download through proxies, use a ~/.wgetrc file or environment variables with the proxy settings for wget, or the equivalent for other download methods.
With this network-based installation method, what gets installed is the currently available versions of packages and programs. This is in contrast with the other installation methods, which are kept stable between public releases. Continuing package updates can be done with tlmgr.
If you have trouble with the installer downloading every package individually, you might find it more reliable to mirror TeX Live to a local directory and then install from that.
Sources: the live network installation does not include the hundreds of megabytes of sources for the compiled programs. The sources for the current release are on CTAN, and historical releases are also available (under systems/texlive; both the initial release each year, and the frozen state at the end of the cycle in tlnet-final), and current development sources are in the repository.
Information about downloading/mirroring the TeX Live archive repository is available separately, as well as other ways to acquire TeX Live.