With the constantly advancing capabilities of quantum computers, conventional cryptographic systems relying on complex math problems may encounter unforeseen vulnerabilities. Unlike regular computers, which are often deemed cost-ineffective in cryptographic attacks, quantum computers have a significant advantage in calculation speed. This distinction potentially makes currently used algorithms less secure or even completely vulnerable, compelling the exploration of post-quantum cryptography (PQC) as the most reasonable solution to quantum threats. This review aims to provide current information on applications, benefits, and challenges associated with the PQC. The review employs a systematic scoping review with the scope restricted to the years 2022 and 2023; only articles that were published in scientific journals were used in this paper. The review examined the articles on the applications of quantum computing in various spheres. However, the scope of this paper was restricted to the domain of the PQC because most of the analyzed articles featured this field. Subsequently, the paper is analyzing various PQC algorithms, including lattice-based, hash-based, code-based, multivariate polynomial, and isogeny-based cryptography. Each algorithm is being judged based on its potential applications, robustness, and challenges. All the analyzed algorithms are promising for the post-quantum era in such applications as digital signatures, communication channels, and IoT. Moreover, some of the algorithms are already implemented in the spheres of banking transactions, communication, and intellectual property. Meanwhile, despite their potential, these algorithms face serious challenges since they lack standardization, require vast amounts of storage and computation power, and might have unknown vulnerabilities that can be discovered only with years of cryptanalysis. This overview aims to give a basic understanding of the current state of post-quantum cryptography with its applications and challenges. As the world enters the quantum era, this review not only shows the need for strong security methods that can resist quantum attacks but also presents an optimistic outlook on the future of secure communications, guided by advancements in quantum technology. By bridging the gap between theoretical research and practical implementation, this paper aims to inspire further innovation and collaboration in the field.