With the rapid development of Lattice-based post-quantum cryptography, algorithms for hard problems in Lattices have become an essential tool for evaluating the security of post-quantum cryptographic schemes. Algorithms such as enumeration, sieve, and Lattice basis reduction have been developed under the classical computing model, while quantum algorithms for solving hard problems in Lattices, such as quantum sieve and quantum enumeration, are gradually attracting attention. Although Lattice problems possess post-quantum properties, techniques such as quantum search can accelerate a range of Lattice algorithms. Given the challenges involved in solving hard problems in Lattices, this study first summarizes and analyzes the research status of quantum algorithms for such problems and organizes their design principles. Then, the quantum computing techniques applied in these algorithms are introduced, followed by an analysis and comparison of their computational complexities. Finally, potential future developments and research directions for quantum algorithms addressing Lattice-based hard problems are discussed.