Models of species distributions aim to describe and often to predict the spatial distribution of individual species, using as a basis the species’ relationship with its environment. At a broad level this can be done in two main ways. The first is to model the processes that underpin where the species occur: demographic or physiological processes that fundamentally define the species distribution. The second and much more common approach is to fit a numerical model that defines the relationships between observations of the species occurrence and any covariates considered relevant. This article focuses on the second, aiming to introduce the reader to key texts and ideas in this large and popular field of modeling whose applications span ecology, biogeography, evolutionary biology, conservation, biosecurity, health, and computation. It focuses on the models and the mapped predictions often derived from them. Referred to as species distribution models (SDMs) here, these (or their variants) are also referred to as ecological niche models, habitat models, or bioclimatic envelope models. Several textbooks have now been published on SDMs, giving good insights into background, theory, applications, data, and models. Thousands of manuscripts are published including those developing new methods, those that apply SDMs to ecological theory and understanding, and those that apply the maps in conservation, planning, and management applications. This bibliography leads the reader through the literature, first covering the background and standard approaches to fitting, evaluating, and reporting SDMs. Then, aiming to extend beyond the information presented thoroughly in existing textbooks, it describes related models that are still correlative and applicable for modeling individual species but that provide important extensions. These allow modelers to deal with the common complexities in data (structured datasets, imperfect detection, spatio-temporal issues) and to broaden the models to include biological processes or issues of interest such as biotic interactions, movement, traits and phylogenetic data.