  It is now well established that laser plasma acceleration (LPA) is an
innovative and good candidate in the beam acceleration field. Relativistic
beams are indeed produced up to several GeV but their quality remains to be
demonstrated in the highly demanding case of Free Electron Lasers (FELs).
Several experiments already showed the feasibility of synchrotron radiation
delivery based on a LPA but free electron lasing has still to be achieved.
Since the quality of the LPA beam inside the undulator is the critical issue,
any LPA based FEL experiment requires a refined characterization of the beam
properties along the transport line and of the photon beam at the undulator
exit. This characterization relies on diagnostics which must be adapted to the
LPA specificities. We will review the electron and photon diagnostics already
used on LPAs and required for LPA based FELs, and illustrate the critical
points using recent experiments performed around the world.
