The use of satellite technology for communication and data transmission has greatly increased in recent years, and low earth orbit (LEO) satellites have become an important part of this infrastructure. LEO satellites orbit the earth at an altitude of around 500 to 2,000 kilometers, which allows them to provide coverage to a larger area compared to higher altitude satellites. However, routing data through LEO satellites presents unique challenges due to their low altitude and the need to continuously adjust their communication links as they move. To address these challenges, various routing algorithms have been developed to optimize the transmission of data through LEO satellite networks. In this review, we will examine the different types of LEO satellite routing algorithms and their key features, as well as the challenges and opportunities they present. We will also discuss the performance and trade-offs of these algorithms and their potential applications in various scenarios.