The reconstruction processes in acoustical tomography have to satisfy several conditions. First, account has to be taken of refraction. Second, account has to be taken of scattering (which is linked to the refraction process). Third, diffraction occurs. Fourth, the sampling of wave fronts by transducers of finite size produces averaging effects which reduce resolution. Fifth, the refractive and scattering effects create a noise problem which limits time of flight measurement resolution. Sixth, the reconstruction times should be less than 1 minute for many applications. These factors are discussed in relation to the conditions found in soft tissue.