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In this paper, we do a critical review of statistical methods for landslide susceptibility modelling and associated terrain zonations. Landslide susceptibility is the likelihood of a landslide occurring in an area depending on local terrain conditions, estimating “where” landslides are likely to occur. Since the first attempts to assess landslide susceptibility in the mid-1970s, hundreds of papers have been published using a variety of approaches and methods in different geological and climatic settings. Here, we critically review the statistically-based landslide susceptibility assessment literature by systematically searching for and then compiling an extensive database of 565 peer-review articles from 1983 to 2016. For each article in the literature database, we noted 31 categories/sub-categories of information including study region/extent, landslide type/number, inventory type and period covered, statistical model used, including variable types, model fit/prediction performance evaluation method, and strategy used to assess the model uncertainty. We present graphical visualisations and discussions of commonalities and differences found as a function of region and time, revealing a significant heterogeneity of thematic data types and scales, modelling approaches, and model evaluation criteria. We found that the range of thematic data types used for susceptibility assessment has not changed significantly with time, and that for a number of studies the geomorphological significance of the thematic data used is poorly justified. We also found that the most common statistical methods for landslide susceptibility modelling include logistic regression, neural network analysis, data-overlay, index-based and weight of evidence analyses, with an increasing preference towards machine learning methods in the recent years. Although an increasing number of studies in recent years have assessed the model performance, in terms of model fit and prediction performance, only a handful of studies have evaluated the model uncertainty. Adopting a Susceptibility Quality Level index, we found that the quality of published models has improved over the years, but top-quality assessments remain rare. We identified a clear geographical bias in susceptibility study locations, with many studies in China, India, Italy and Turkey, and only a few in Africa, South America and Oceania. Based on previous literature reviews, the analysis of the information collected in the literature database, and our own experience on the subject, we provide recommendations for the preparation, evaluation, and use of landslide susceptibility models and associated terrain zonations.