  Modelling, analysing and inferring triggering mechanisms in population
reproduction is fundamental in many biological applications. It is also an
active and growing research domain in mathematical biology. In this chapter, we
review the main results developed over the last decade for the estimation of
the division rate in growing and dividing populations in a steady environment.
These methods combine tools borrowed from PDE's and stochastic processes, with
a certain view that emerges from mathematical statistics. A focus on the
application to the bacterial cell division cycle provides a concrete
presentation, and may help the reader to identify major new challenges in the
field.
