Landslides are recognized as a generation mechanism of tsunamis. While earthquake-generated tsunamis are catastrophes on a more global scale, landslide-generated tsunamis tend to cause extreme local damage. Acknowledging the great uncertainty in the motion and the properties of real tsunamigenic landslides, and the challenges in assuming a complex multiphysics landslide model given the uncertainty, we focus on understanding the fundamental mechanics of the wave generation process. The main objectives of this study are to determine the most computationally efficient wave model that can be used to simulate the wave generation process due to a submarine landslide, and to construct a closed-form wave generation model that requires no computation. New analytical solutions were derived for landslide-generated tsunamis in idealized scenarios. Analytical solutions not only provide the scaling relations between a submarine landslide and the resulting tsunami, but also reveal that the volume of a landslide, as opposed to its exact shape, has the greatest impact on the leading tsunami wave generated by the landslide. Therefore, in modeling, it is more important to match the landslide volume than to match the exact landslide shape. Numerical solvers based on long-wave equations were constructed to complement the analytical solutions. By comparing the numerical results based on different long-wave equations, nonlinear effects and frequency dispersion effects were examined separately. Using the knowledge gained from both analytical solutions and numerical simulations, we proposed criteria to determine whether nonlinearity is important and whether frequency dispersion is important in a landslide tsunami problem, and therefore the appropriate wave generation model to use. Lastly, combining the findings of this study, we constructed a closed-form landslide tsunami generation model. As a function of relevant input parameters, the model outputs a tsunami wave profile due to a submarine landslide. In contrast to all existing closed-form landslide tsunami generation models, the new model is based on the newly derived analytical solutions, and provides information on not only the maximum wave height, but also the complete free surface profile, the flow velocity, and the duration of the wave generation stage. The new model was shown to be an improvement over a commonly used empirical model.