  The run-and-tumble dynamics of bacteria, as exhibited by \textit{E. coli},
offers a simple experimental realization of non-Brownian, yet diffusive,
particles. Here we present some analytic and numerical results for models of
the ideal (low-density) limit in which the particles have no hydrodynamic or
other interactions and hence undergo independent motions. We address three
cases: sedimentation under gravity; confinement by a harmonic external
potential; and rectification by a strip of `funnel gates' which we model by a
zone in which tumble rate depends on swim direction. We compare our results
with recent experimental and simulation literature and highlight similarities
and differences with the diffusive motion of colloidal particles.
