The fifth generation (5G) wireless communication systems have been deployed around the world, and the sixth generation (6G) networks have become the focus of research interest, whose technical roadmap has been put forward. Low earth orbit (LEO) satellite communication, which is expected to bridge the digital divide and provide ubiquitous access for mobile terminals anytime and anywhere, will play an important role in 6G and beyond networks. LEO satellite communications help to achieve the key performance indicators as specified in emerging 6G applications. In addition, 6G technologies such as Tera Hertz, digital twin, intelligent reflecting surface, artificial intelligence, etc., also create many new applications for LEO satellite communications. This article aims to provide a comprehensive overview on LEO satellite communications in 6G and beyond mobile networks from the perspectives of its technologies, applications, and challenges.