Landslide-generated waves (LGWs) are among natural hazards that have stimulated attentions and concerns of engineers and researchers during the past decades. At the same period, the application of numerical modeling has been progressively increased to assess, control, and manage the risks of such hazards. This paper represents an overview of numerical studies on LGWs to explore associated recent advances and future challenges. In this review, the main landslide events followed by an LGW hazard are scrutinized. The uncertainty regarding landslide characteristics and the lack of data concerning generated tsunami properties highlights the necessity of probabilistic analysis and numerical modeling. More than 53 % of landslides show the slide length larger than about 20 times of the slide thickness. This fact justifies the popular application of depth-averaged equations (DAEs) for landslides’ motion simulations. Such models are reviewed and tabulated based on their mathematical, numerical, and conceptual approaches. A landslide is generally treated as a homogeneous, mixture, or a multi-phase fluid with different rheologies. The Coulomb type rheology is the most-used rheology applied in more than 70 % of landslide models. Some of the recent studies are considering the effects of multi-phase nature, dynamic changes of rheological parameters, and grain-size segregation of the landslide on its deformations. The numerical tools that model LGWs are also reviewed, categorized, and examined. These models conceptualize a landslide as a general rigid LGW (R-LGW) or deformable LGW (D-LGW) mass. The rigid slide assumption is mainly applied in the LGW models with a focus on the accurate simulation of the wave propagation stage, particularly by means of higher order Boussinesq-type wave equations (BWEs). The majority of D-LGW models solve either the Navier–Stokes equations (NSEs) for a multi-phase (landslide material, water, and air) flow or the shallow water equations (SWEs) for a two-layer (a layer of granular material moving beneath a layer of water) flow. NSEs are more comprehensive models but less robust than DAEs. The key effect of dispersion in LGWs, which are typically important in intermediate and even deep water wave domains, challenges researchers to apply higher order BWEs instead of SWEs in two-layer models. Regarding numerical approaches, Lagrangian’s are more robust than Eulerian’s, but they have been rarely applied due to their high computational demands for real cases. The remaining challenges are reviewed as the necessity of probabilistic analysis to assess the risk of the related hazards more accurately for both past and potential LGW hazards; further thorough laboratory-scale experiments and field data measurements to have accurate and detailed benchmark data; providing RS/GIS-based worldwide hazard map for potential LGWs and compiled database for occurred events; extending BWEs for granular flows and DAEs with non-hydrostatic corrections; and economizing the computational costs of models by advanced techniques like parallel processing and GPU accelerators.