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The way the media presents events can significantly affect public perception, which in turn can alter people's beliefs and views. Media bias describes a one-sided or polarizing perspective on a topic. This article summarizes the research on computational methods to detect media bias by systematically reviewing 3140 research papers published between 2019 and 2022. To structure our review and support a mutual understanding of bias across research domains, we introduce the Media Bias Taxonomy, which provides a coherent overview of the current state of research on media bias from different perspectives. We show that media bias detection is a highly active research field, in which transformer-based classification approaches have led to significant improvements in recent years. These improvements include higher classification accuracy and the ability to detect more fine-granular types of bias. However, we have identified a lack of interdisciplinarity in existing projects, and a need for more awareness of the various types of media bias to support methodologically thorough performance evaluations of media bias detection systems. Concluding from our analysis, we see the integration of recent machine learning advancements with reliable and diverse bias assessment strategies from other research areas as the most promising area for future research contributions in the field.