With the advent of computers and quantum algorithms, the security of current public key cryptography systems can face challenges. Breaking the current cryptographic structures would require multi-million qubit quantum computers, which have not yet been built; however, with significant advancements in quantum technology by leading companies in this field and the concern within the cryptography community, there has been a felt need to quickly provide countermeasures. In 2016, the National Institute of Standards and Technology (NIST) sought proposals from around the world to standardize post-quantum cryptographic schemes to address this issue. At that time, the McEliece code-based encryption system (and its equivalent Niederreiter system), despite being proven resistant to both classical and quantum algorithms, was not accepted due to its large public keys. Ultimately, the Classic McEliece, HQC, and BIKE encryption systems, which fall under code-based cryptography, advanced to the final stage of these competitions, and the winners of this cryptographic category will be announced by the end of 2024. This paper aims to review the developments made to optimize code-based structures and to examine the selected code-based cryptographic schemes and the latest status of Classic McEliece standardization.