Well, after a long time, NIST announced the first four quantum-resistant cryptographic algorithms.
Both of my StarTrek inspired favorites are actually in. CRYSTALS-Kyber is the one selected for a key exchange purposes and I fully expect to see it in some future OpenSSH version. Since dealing with ED25519 would require a quantum computer much bigger than currently available, eliptic curves are still probably the best default choice. However, you don't want to wait the last moment to switch. Considering there are still some system that only support RSA (yes Mikrotik, I'm talking about you), switch will take a while.
CRYSTALS-Dilithium, a part of the same family, got selected as one of three suggested digital signature algorithms. From practicality side, it will rarely, if ever, be used alone as its signature output is literaly larger than a KB. That said, there are a few suggested modes (e.g. Dilithium3-AES) keeping the reasonable key size AES provides while retaining quantum assurances of a lattice algorthm.
FALCON was also selected despite difficulty of a correct implementation and a huge potential for side-channel attacks. I guess a small memory footprint and impressive performance in embedded applications were enough to ensure its place among finalists.
Lastly, a SPHINCS+ came out of blue (at least for me) to take its place as the last of the finalists. Since it is slower and larger than either of the other two finalists, it's hardly a first choice. Regardless, using a different math approach compared to other two finalists was valuable enough to get it in.
NewHope, one of the round two finalists and already used by Chrome ended up like the recent Star Wars sequels. An early succes but ultimately not good enough to pursue.