Chemotaxis is a fundamental process in the life of many prokaryotic and eukaryotic cells. Chemotaxis of bacterial populations has been modeled by both individual-based models that take into account the biochemistry of intracellular signaling, and continuum PDE models that track the evolution of the cell density in space and time. Continuum models have recently been derived from individual-based models under different assumptions. In this talk I will give an overview of the results along this line and discuss recent progress we made.