Bacteria navigating through a chemotactic gradient in their natural habitats or in large bioreactors are under the influence of noise (or fluctuations) inside the cells, at the interfaces of the chemical ligands with the chemoreceptors, and in the external environment that contains the chemoattractant. These sources of noise interact with one another and may strongly affect the chemotactic motility of the cells. Although bacteria have evolved filtering mechanisms, mainly through feedback loops, for intracellular noise and receptor-ligand binding noise, external filters are required for environmental noise. With Escherichia coli as a model system, these aspects are reviewed in terms of their effects on the chemosensory network, models for the filters, and optimization of Chemotaxis under noise-affected conditions. It is suggested that stochastic resonance may be a key feature determining the design of an optimal filtering strategy that encompasses all sources of noise.