In this talk, we are concerned with the nonlinear logaritimic Schrodinger equations. When the potential satisfies a global assumption, we give the multiple solu- tions. When the potential satisfies a local assumption, due to del Pino and Felmer, we consider the existence and concentration of positive solutions. Then, based on some new estimates from previous research, the multi-bump solutions are obtained for a logarithmic Schrodinger equation with deepening potential well. This talk is based on joint works with Professor Claudianor O. Alves.