Engagement during human-robot first encounters is a challenging task that requires both parties to understand each other’s intent to interact without mutual information. Engagement may fail due to people’s unawareness of the robot’s presence and its desire to interact, or because of people’s lack of interest in interacting. In this thesis, we pursue answers to the following research question: “Which theories and methods can enhance the way a mobile social robot engages with humans in first encounters to increase engagement success and improve people’s perceptions of the robot?”. We concentrate on one-to-one human-robot nonverbal interactions during first encounters with cognitively healthy adults and in public or semi-public places. We explore whether human-human greeting models from social psychology can be an answer to this question. First, we surveyed existing engagement models for mobile robots, analyzed the state-of-the-art of technological solutions for human-robot engagement, and proposed a taxonomy to organize the literature according to well-known greeting models. On the technological side, we developed handshake skills for the Vizzy robot, a pipeline to detect social signals, and methods to detect interaction errors. Our first user study confirmed the social agency of the Vizzy robot and showed how people interact with it. Then, we gathered support for our hypothesis by evaluating a handshake salutation (part of human-human greeting models). People reported increased intentions to help the robot in the future after greetings with a handshake, and increased perceived warmth, likeability, and animacy. The final experiment tested three different greeting models with ablations of a human-human greeting model proposed by Kendon. When the robot acted with the entire model, its interaction intentions were clearer to the human than when only a subset of the model was used, thus empirically demonstrating that a human-human greeting model, namely Kendon’s model, is effective in human-robot engagement.