Recent advances in machine intelligence and robotics have enabled new forms of human-computer interaction characterized by greater adaptability, shared decision-making, and mixed initiative. These advances are leading toward machines that can operate with relative autonomy but are designed to interact or engage with human counterparts in joint human-machine teams. The degree to which people trust machines is critical to the efficacy of these teams. People will cooperate with, and rely upon, intelligent agents they trust. Those they do not trust fall into disuse. As intelligent agents become more self-directed, learn from their experiences, and adapt behavior over time, the relationship between people and machines becomes more complex, and designing system behaviors to engender the proper level of trust becomes more challenging. Moreover, as intelligent systems become common in safety-critical domains, we must understand and assess the influence they might exert on human decision making to avoid unintended consequences, such as over-trust, compliance, or undue influence. Online social environments further complicate human-machine relationships. In the social media ecosystem, intelligent agents (e.g., chatbots) might act as aids or assistants but also as competitors or adversaries. In this context, research challenges include understanding how human-machine relationships evolve in social media and especially how humans develop trust and are susceptible to influence in social networks. This special issue explores research frontiers in intelligent human-machine interaction with a special focus on trust and influence. It includes a selection of seven articles that make key