The recent entry into the market of some advanced iterative reconstruction algorithms (IA) optimized for bone and cardiac studies has raised a great interest among specialists in nuclear medicine. In particular, myocardial perfusion studies have received a significant boost thanks to the superior quality of images obtained with these new reconstruction methods. Differently from the filtered back-projection (FBP), the basic principles of the iterative reconstruction techniques are less known; unclear is the way by which the iterative methods are able to include compensations for the main degradation phenomena in SPECT imaging. Aim of this review is to provide a simple introduction to the iterative solution of the tomographic problem by using its matricial representation. This paper will also provide simple graphical examples of how phenomena such as attenuation and depth dependent resolution can be modelled in the projection operator. The main degrading factors in cardiac SPECT images will be retrieved along with some indication of the effectiveness of the corrections adopted. This step makes clear the noteworthy qualitative improvement obtained with these advanced algorithms. A brief summary of the main features of the most widespread new iterative reconstruction algorithms will be presented. The majority of manufacturers emphasize the reduction of acquisition times allowed by these innovative algorithms. Finally, because of the awareness of the increasing exposure of the population due to the increasing number of imaging studies with ionizing radiation, the use of these advanced algorithms to achieve a simultaneous reduction in patient dose and acquisition time will be also shown.