Several technical developments have led to a comeback of the continuous scintillators in positron emission tomography (PET). Important differences exist between the resurgent continuous scintillators and the prevailing pixelated devices, which can translate into certain advantages of the former over the latter. However, if the peculiarities of the continuous scintillators are not considered in the iterative reconstruction in which the measured data is converted to images, these advantages will not be fully exploited. In this paper, we review which those peculiarities are and how they have been considered in the literature of PET reconstruction. In light of this review, we propose a new method to compute one of the key elements of the iterative schemes, the system matrix. Specifically, we substitute the traditional Gaussian approach to the so-called uncertainty term by a more general Monte Carlo estimation, and account for the effect of the optical photons, which cannot be neglected in continuous-scintillators devices. Finally, we gather in a single scheme all the elements of the iterative reconstruction that have been individually reformulated, in this or previous works, for continuous scintillators, providing the first reconstruction framework fully adapted to this type of detectors. The preliminary images obtained for a commercially available PET scanner show the benefits of adjusting the reconstruction to the nature of the scintillators.