  The reconstruction task in photoacoustic tomography can vary a lot depending
on measured targets, geometry, and especially the quantity we want to recover.
Specifically, as the signal is generated due to the coupling of light and sound
by the photoacoustic effect, we have the possibility to recover acoustic as
well as optical tissue parameters. This is referred to as quantitative imaging,
i.e, correct recovery of physical parameters and not just a qualitative image.
In this chapter, we aim to give an overview on established reconstruction
techniques in photoacoustic tomography. We start with modelling of the optical
and acoustic phenomena, necessary for a reliable recovery of quantitative
values. Furthermore, we give an overview of approaches for the tomographic
reconstruction problem with an emphasis on the recovery of quantitative values,
from direct and fast analytic approaches to computationally involved
optimisation based techniques and recent data-driven approaches.
