Lattice public key cryptography is widely conceived as the most promising candidate in the quantum computing era due to the averagecase / hardcase equivalence of the underlying mathematic cally intractable problems, the linearity of the involved algebraic structures, and the tremendous cryp tographic functionalities. At present, numerous post quantum lattice cryptographic algorithms were deeloped to rely their securities on a lattice problem: the learning with errors ( LWE) problem. There fore, it is of vital significance to study the algorithms for solving the LWE problems to give insights in to the security of lattice public key cryptography. This paper firstly reviews and compares different solution strategies for distinct types of LWE problems. Secondly, we outline the basic ideas and technical principles of the existing lattice reduction algorithms. Finally, some prospections are made on the research focuses and trends in solving the LWE problems with lattice based reduction algorithms.