The manifestation and effect of bias in news reporting have been central topics in the social sciences for decades, and have received increasing attention in the NLP community recently. While NLP can help to scale up analyses or contribute automatic procedures to investigate the impact of biased news in society, we argue that methodologies that are currently dominant fall short of addressing the complex questions and effects addressed in theoretical media studies. In this survey paper, we review social science approaches and draw a comparison with typical task formulations, methods, and evaluation metrics used in the analysis of media bias in NLP. We discuss open questions and suggest possible directions to close identified gaps between theory and predictive models, and their evaluation. These include model transparency, considering document-external information, and cross-document reasoning rather than single-label assignment.

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