  Monte Carlo algorithms have a growing impact on nuclear medicine
reconstruction processes. One of the main limitations of myocardial perfusion
imaging (MPI) is the effective mitigation of the scattering component, which is
particularly challenging in Single Photon Emission Computed Tomography (SPECT).
In SPECT, no timing information can be retrieved to locate the primary source
photons. Monte Carlo methods allow an event-by-event simulation of the
scattering kinematics, which can be incorporated into a model of the imaging
system response. This approach was adopted since the late Nineties by several
authors, and recently took advantage of the increased computational power made
available by high-performance CPUs and GPUs. These recent developments enable a
fast image reconstruction with an improved image quality, compared to
deterministic approaches. Deterministic approaches are based on
energy-windowing of the detector response, and on the cumulative estimate and
subtraction of the scattering component. In this paper, we review the main
strategies and algorithms to correct for the scattering effect in SPECT and
focus on Monte Carlo developments, which nowadays allow the three-dimensional
reconstruction of SPECT cardiac images in a few seconds.
