From the Federal Register:

After three rounds of evaluation and analysis, NIST selected four algorithms it will standardize as a result of the PQC Standardization Process. The public-key encapsulation mechanism selected was CRYSTALS-KYBER, along with three digital signature schemes: CRYSTALS-Dilithium, FALCON, and SPHINCS+.

These algorithms are part of three NIST standards that have been finalized:

• FIPS 203: Module-Lattice-Based Key-Encapsulation Mechanism Standard
• FIPS 204: Module-Lattice-Based Digital Signature Standard
• FIPS 205: Stateless Hash-Based Digital Signature Standard

NIST press release. My recent writings on post-quantum cryptographic standards.

EDITED TO ADD: Good article:

One – ML-KEM [PDF] (based on CRYSTALS-Kyber) – is intended for general encryption, which protects data as it moves across public networks. The other two –- ML-DSA [PDF] (originally known as CRYSTALS-Dilithium) and SLH-DSA [PDF] (initially submitted as Sphincs+)—secure digital signatures, which are used to authenticate online identity.

A fourth algorithm – FN-DSA [PDF] (originally called FALCON) – is slated for finalization later this year and is also designed for digital signatures.

NIST continued to evaluate two other sets of algorithms that could potentially serve as backup standards in the future.

One of the sets includes three algorithms designed for general encryption – but the technology is based on a different type of math problem than the ML-KEM general-purpose algorithm in today’s finalized standards.

NIST plans to select one or two of these algorithms by the end of 2024.

IEEE Spectrum article.

Slashdot thread.