Toponym is an essential element of geospatial information. Traditionally, toponyms are collected in a gazetteer through field surveys that require significant resources, including labor, time, and money. Nowadays, we can utilize social media and online news portals to collect event locations or toponyms from the text. This article presents a survey of studies that focus on the extraction and disambiguation of toponyms from textual documents. While toponym extraction aims to identify toponyms from the text, toponym disambiguation determines their specific locations on the earth. The survey covered articles published between January 2015 and April 2023, presented in English, and gathered from five major journal databases. The survey was conducted by adopting the Kitchenham guidelines, consisting of an initial article search, article selection, and annotation process to facilitate the reporting phase. We employed Mendeley as a reference management tool and NVivo to categorize certain parts of the articles that are the focal points of interest in this survey. The primary focus of the survey was on the methods or approaches performed in the research articles to extract and disambiguate toponyms. Additionally, we also discuss some general challenges in toponym research, different applications for toponym extraction and disambiguation, data sources, and the use of languages other than English in the studies. The survey confirms that each approach has its limitations. Extracting and disambiguating toponyms from text is complex and challenging, especially for low-resource languages. We also suggest some research directions related to toponym extraction and disambiguation that could enrich the gazetteer.