Malware still constitutes a major threat in the cybersecurity landscape, also due to the widespread use of infection vectors such as documents. These infection vectors hide embedded malicious code to the victim users, facilitating the use of social engineering techniques to infect their machines. Research showed that machine-learning algorithms provide effective detection mechanisms against such threats, but the existence of an arms race in adversarial settings has recently challenged such systems. In this work, we focus on malware embedded in PDF files as a representative case of such an arms race. We start by providing a comprehensive taxonomy of the different approaches used to generate PDF malware, and of the corresponding learning-based detection systems. We then categorize threats specifically targeted against learning-based PDF malware detectors, using a well-established framework in the field of adversarial machine learning. This framework allows us to categorize known vulnerabilities of learning-based PDF malware detectors and to identify novel attacks that may threaten such systems, along with the potential defense mechanisms that can mitigate the impact of such threats. We conclude the paper by discussing how such findings highlight promising research directions towards tackling the more general challenge of designing robust malware detectors in adversarial settings.