The present level of proliferation of fake, biased, and propagandistic content online has made it impossible to fact-check every single suspicious claim or article, either manually or automatically. Thus, many researchers are shifting their attention to higher granularity, aiming to profile entire news outlets, which makes it possible to detect likely fake news the moment it is published, by simply checking the reliability of its source. Source factuality is also an important element of systems for automatic fact-checking and fake news detection, as they need to assess the reliability of the evidence they retrieve online. Political bias detection, which in the Western political landscape is about predicting left-center-right bias, is an equally important topic, which has experienced a similar shift towards profiling entire news outlets. Moreover, there is a clear connection between the two, as highly biased media are less likely to be factual; yet, the two problems have been addressed separately. In this survey, we review the state of the art on media profiling for factuality and bias, arguing for the need to model them jointly. We further discuss interesting recent advances in using different information sources and modalities, which go beyond the text of the articles the target news outlet has published. Finally, we discuss current challenges and outline future research directions.