The security of resource-constrained devices is critical in the IoT field, given that everything is interconnected. Therefore, the National Institute of Standards and Technology (NIST) initialized the lightweight cryptography (LWC) project to standardize the lightweight cryptography algorithms for resource-constrained devices. After two rounds, the NIST announced the finalists in 2021. The finalist algorithms are Ascon, Elephant, GIFT-COFB, Grain-128AEAD, ISAP, PHOTON-Beetle, Romulus, SPARKLE, TinyJambu, and Xoodyak. The final round of the competition is still in progress, and the NIST will select the winner based on their and third-party evaluations. In this paper, we review the 10 finalists mentioned above, discuss their constructions, and classify them according to the underlying primitives. In particular, we analyze these ciphers from different perspectives, such as cipher specifications and structures, design primitives, security parameters, advantages and disadvantages, and existing cryptanalyses. We also review existing analyses of these finalists with a specific focus on the review of fault attacks. We hope the study compiled in this paper will benefit the cryptographic community by providing an easy-to-grasp overview of the NIST LWC finalists.