Understanding the transition to turbulence at a concrete
level has great importance both conceptually and practically.
Once put in the realm of dynamical systems theory by
Ruelle and Takens (1971), the problem can be considered
as essentially solved for systems like Rayleigh-B\'enard
convection experiencing a progressive and continuous,
globally supercritical growth of disorder. For open flows,
difficulties arise when there is no relevant linear
instability mechanism to explain the wilder form of
transition to turbulence that then takes place via
coexisting domains of laminar and turbulent flow.
I will give a brief overview of the situation and discuss
the currently developed paths followed to improve our
understanding, fr　om the search for exact solutions of
the Navier-Stokes equations within dynamical systems
theory to tentative modeling in terms of stochastic
systems of use in statistical physics.