This study presents a review of research on social media bot detection. Social media bots are used by political and criminal actors for mass distribution of political messages, as well as rumors, conspiracy theories, and other forms of false information. Through the spread of disinformation, bots are eroding the public trust in political and media institutions and integrity of social media. We have examined recent research publication in the field of social media bot detection, including several previous reviews of bot detection research, and identified the methods used in bot detection and issues encountered by researchers. Our review was conducted through a search of 5 main bibliographical databases, which has produced a total of 534 research papers and other publications. This collection was then filtered with exclusion and inclusion criteria to isolate the most pertinent documents, resulting in a focused selection of 49 documents that were analyzed for this review. In the first part of the paper we introduce the phenomenon of fake news within social networks, its connection with social media bot activity, and conclude the introduction with issues caused or exacerbated by bots. In the main part of this paper we first present the results of statistical analysis of the reviewed documents and then introduce the field of social media bot research, followed by an overview of the issues of social media bot detection identified in the reviewed literature, including the evolution of bot concealment techniques and the methodological issues presented in some of the bot detection studies. We then proceed with an overview of the methods and results from the reviewed research papers, structured according to the main methodology used in the examined studies. Our review concludes with examination of the recent trends in social media bot development and related bot detection research.