  We consider image reconstruction in full-field photoacoustic tomography,
where 2D projections of the full 3D acoustic pressure distribution at a given
time T>0 are collected. We discuss existing results on the stability and
uniqueness of the resulting image reconstruction problem and review existing
reconstruction algorithms. Open challenges are also mentioned. Additionally, we
introduce novel one-step reconstruction methods allowing for a variable speed
of sound. We apply preconditioned iterative and variational regularization
methods to the one-step formulation. Numerical results using the one-step
formulation are presented, together with a comparison with the previous
two-step approach for full-field photoacoustic tomography
