At the individual scale, bacteria as E. colimove by perform-ing so-called run-and-tumble movements. This means that they alternate ajump (run phase) followed by fast re-organization phase (tumble) in whichthey decide of a new direction for run. For this reason, the population is described by a kinetic-Botlzmann equation of scattering type. Non linearityccurs when one takes into account chemotaxis, the release by the individualcells of a chemical in the environment and response by the population.These models can explain experimental observations, fit precise measure-ments and sustain various scales. They also allow to derive, in the diffusionlimit, macroscopic models (at the population scale), as the Flux-Limited-Keller-Segel system, in opposition to the traditional Keller-Segel system, thismodel can sustain robust traveling bands as observed in Adler’s famous experiment. Furthermore, the modulation of the tumbles, can be understood using intra cellular molecular pathways. Then, the kinetic-Boltzmann equation canbe derived with a fast reaction scale. Long runs at the individual scale andabnormal diffusion at the population scale, can also be derived mathematically.