Tourism represents one of the main industries in terms of job creation and economic development while sustainability in tourism represents a worldwide challenge. The objective of the present study is to use a bibliometric approach to review the relevant literature. Bibliometric indicators, such as citations, are used to identify the field structure and the VOSviewer software is used to map the main trends in this area. Over the period 1987–2018, a total of 4647 papers were found in Scopus regarding sustainability issues in tourism. Analysis of the leading journals, authors, institutions, and keywords indicates that: (1) the literature on sustainability issues in the field of tourism is significantly growing; (2) a mere six papers accounted more than 300 citations, but there are several prolific authors; (3) of the 614 sources included in the review, the most important have published 46.7% of the papers; (4) in terms of documents and citations, the United States is the leading country in this topic; (5) according to keyword trend network analysis, sustainability is becoming a strategic approach for companies and tourist destinations. Finally, this subfield within the tourism literature has considerable potential and is expected to continue growing.