Chemotaxis models are used to describe the movements of mobile species or living organisms in response to certain chemicals in their environments. The current talk is concerned with various dynamical aspects of chemotaxis models with logistic source on the whole space. I will first discuss the global existence of positive classical solutions of such chemotaxis models, which is fundamental for the study of various dynamical aspects. Next, I will discuss the asymptotic behavior of globally defined positive solutions with strictly positive initial functions. I will then consider the spatial spreading dynamics of positive solutions with compactly supported or front-like initial functions.