In this work, global existence and large time behavior of solutions in chemotaxis systems are considered. We first focus on the fully parabolic Keller-Segel model and investigate a sufficient condition for the existence of global solutions. The boundedness and global existence of solutions in a chemotaxis-haptotaxis model are also demonstrated under suitable assumptions on the parameters. Similarly, the long time behavior in a Keller-Segel model with logistic dampening is identified. Particularly, when the logistic Keller-Segel model is without growth term and is coupled with an additional convection term, an optimal decay estimate is given. In addition, the existence of classical solutions of a chemotaxis-Navier-Stokes model in the two- and three-dimensional cases is obtained under suitable smallness conditions on the initial data.