The spin - crossover compounds (SCO) have become of great interest recently due to their potential applications in memories, sensors, switches, and display devices. These materials are particularly interesting because upon application of heat, light, pressure or other physical stimulus, they feature a phase transition between a low-spin (LS) diamagnetic ground state and a high-spin (HS) paramagnetic state, accompanied in some cases by color change. The phase transition can be discontinuous (with hysteresis), in two steps or gradual. Our analysis is performed by using the atom - phonon coupling (APC) model which considers that neighboring molecules are connected through a spring characterized by an elastic constant depending on molecules electronic state. By associating a fictitious spin to each molecule that has -1 and +1 eigenvalues corresponding to LS and HS levels respectively, an Ising type model can be developed for the analysis of metastable states and phase transitions in spin-crossover compounds. This contribution is aimed at providing a review of our recent results in this area, as well as novel aspects related to SCO compounds behavior at low temperature. In the framework of the APC model, we will discuss about the existence of metastable and unstable states, phase transitions and hysteresis phenomena, as well as their dependence on sample size. © Published under licence by IOP Publishing Ltd.