We currently use the sha512crypt algorithm for storing the password for tlwebadm. This algorithm is very popular on Linux systems and is still the default algorithm for /etc/shadow.
However it is starting to show its age and it is not very good at protecting against GPU and ASIC attacks. The crypt(5) man page calls it "acceptable" for new hashes rather than "recommended".
(It also states that the default cost of 5000 is too low for modern machines, which is another issue.)
The state-of-the-art seems to be the Argon2 algorithm, but it has yet to be formalised with a crypt() format. However the scrypt algorithm, and some derivatives, are more properly included.
A somewhat inflammatory blog post about current algorithms:
(In reply to Pierre Ossman from comment #0)
> (It also states that the default cost of 5000 is too low for modern
> machines, which is another issue.)
As a counter point, DISA thinks that 5000 is the lower limit, but good enough, in their STIG for RHEL 8.