Surgical simulators present a safe and potentially effective method for surgical training, and can also be used in robot-assisted surgery for pre- and intra-operative planning. Accurate modeling of the interaction between surgical instruments and organs has been recognized as a key requirement in the development of high-fidelity surgical simulators. Researchers have attempted to model tool-tissue interactions in a wide variety of ways, which can be broadly classified as (1) linear elasticity-based, (2) nonlinear (hyperelastic) elasticity-based finite element (FE) methods, and (3) other techniques not based on FE methods or continuum mechanics. Realistic modeling of organ deformation requires populating the model with real tissue data (which are difficult to acquire in vivo) and simulating organ response in real time (which is computationally expensive). Further, it is challenging to account for connective tissue supporting the organ, friction, and topological changes resulting from tool-tissue interactions during invasive surgical procedures. Overcoming such obstacles will not only help us to model tool-tissue interactions in real time, but also enable realistic force feedback to the user during surgical simulation. This review paper classifies the existing research on tool-tissue interactions for surgical simulators specifically based on the modeling techniques employed and the kind of surgical operation being simulated, in order to inform and motivate future research on improved tool-tissue interaction models.