The level of the vibrations and the presence of instability are the two most critical aspects regarding the operations of turbomachinery. To cope with this issues that may compromise the operation of the machines, squeeze film dampers (SFD) are often used in many industrial applications. Unfortunately, many complex phenomena characterize the dynamic behavior of these components and determine the high complexity of the modeling of these components. The most relevant phenomena involved in the characterization of SFDs are individuated after a comprehensive investigation of the state of the art. Among them, the oil film cavitation, the air ingestion, and the effect of the inertia are introduced. A modeling strategy based on the Reynolds equation is then presented. The boundary conditions to be adopted for the feeding and discharging of oil are investigated and implemented. Eventually, the finite difference model is applied to a practical example to evaluate the possibility to minimize the vibration level and to reduce the effect of the instability if a SFD is added to a rotodynamic system. Meaningful information about the modeling of SFDs is provided in this work. The critical aspects of these components and their modeling are highlighted and discussed.