Chemotaxis models are used to describe the movements of mobile species or living organisms in response to certain chemicals in their environments. While chemotaxis models have been extensively investigated in the last four decades, the area remains as one of the most active ones in nonlinear PDEs. In the current talk, I will present some recent progress on front propagation dynamics in chemotaxis models with logistic source on RN. I will first identify the circumstances under which positive classical solutions of such chemotaxis models exist globally, which is fundamental for the study of front propagation dynamics as well as many other dynamical features. Next, I will discuss the asymptotic stability of nonzero constant equilibria of such chemotaxis models, which also plays a role in the study of front propagation dynamics. I will then consider the spreading properties of positive solutions with compactly supported or front-like initial functions. Throughout the talk, special attention will be given to the combined effect of the chemotaxis sensitivity and the logistic damping on the above dynamical issues, in particular, on the speed of traveling wave solutions.

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