Quantum algorithms are a breakthrough in Quantum Computing with the potential to solve complex problems in various fields. This article discusses algorithms like Shor's and Grover's, and their applications in cryptography, optimization, and to the quantum world. However, quantum algorithms face challenges such as error correction and limited applicability. Future advancements will require interdisciplinary research, new algorithms, improved error correction, and better quantum hardware. In this article, we hope to give a brief overview of these algorithms.