Depth-integrated wave models are widely used for simulating large-scale propagation of landslide tsunamis, with the generation of tsunami being simulated separately by various generation models to provide the required initial conditions. For a given problem, the selection of a proper tsunami generation model is an important aspect for tsunami hazard analysis. The generation of tsunamis by submarine or subaerial landslides is a transient multiphase process which involves important fine-scale physics. Depth-integrated generation models, while relatively easy to use, cannot simulate these fine-scale physics. Depth-resolved generation models can overcome the shortcomings of depth-integrated generation models but are computationally demanding. This paper first reviews existing depth-integrated generation models to show the need for depth-resolved generation models. Four classes of depth-resolved generation models are reviewed: computational fluid dynamics (CFD) models, approaches coupling CFD and discrete element method, multiphase flow models, and meshless particle models. Multiphase flow models, which are relatively new, can consider complex interactions between landslide materials and its surrounding fluids. Meshless particle models are appealing for simulating landslide tsunamis because of their convenience to deal with the violent motion of the water surface and ability to run on graphics processing units. The main strengths, weaknesses, and future research directions of the reviewed models are briefly discussed. The literature reviewed, which is by no means complete, aims to provide researchers updated and practical guidelines on numerical modeling techniques for simulating the generation process of landslide tsunamis.