Chemotaxis models describe the movement of cells or organisms in response to chemical signals. In this talk, I will discuss a parabolic-parabolic chemotaxis system with a logistic source and chemical consumption. For both linear and nonlinear diffusion, we prove global existence and boundedness of solutions that are not necessarily integrable. In the linear diffusion case, we show that chemicals generally do not slow down the spreading of cells and, under certain conditions, do not enhance the spreading as well. A key analytical insight is a new relation between cell density and chemical concentration. Numerical simulations also reveal a striking phase transition driven by the chemical sensitivity constant. These are joint work with Zulaihat Hassan (PhD student) and Wenxian Shen.