Network covert channels are increasingly used to endow malware with stealthy behaviors, for instance to exfiltrate data or to orchestrate nodes of a botnet in a cloaked manner. Unfortunately, the detection of such attacks is difficult as network covert channels are often characterized by low data rates and defenders do not know in advance where the secret information has been hidden. Moreover, neutralization or mitigation are hard tasks, as they require to not disrupt legitimate flows or degrade the quality perceived by users. As a consequence, countermeasures are tightly coupled to specific channel architectures, leading to poorly generalizable and often scarcely scalable approaches. In this perspective, this paper investigates trends and challenges in the development of countermeasures against the most popular network covert channels. To this aim, we reviewed the relevant literature by considering approaches that can be effectively deployed to detect general injection mechanisms or threats observed in the wild. Emphasis has been put on enlightening trajectories that should be considered when engineering mitigation techniques or planning the research to face the increasing wave of information-hiding-capable malware. Results indicate that many works are extremely specialized and an effective strategy for taming security risks caused by network covert channels may benefit from high-level and general approaches. Moreover, mechanisms to prevent the exploitation of ambiguities should be already considered in early design phases of both protocols and services.