Brain-robot interaction (BRI) empowers individuals to control (semi-)automated machines through brain activity, either passively or actively. In the past decade, BRI systems have advanced significantly, primarily leveraging electroencephalogram (EEG) signals. This article presents an up-to-date review of 87 curated studies published between 2018 and 2023, identifying the research landscape of EEG-based BRI systems. The review consolidates methodologies, interaction modes, application contexts, system evaluation, existing challenges, and future directions in this domain. Based on our analysis, we propose a BRI system model comprising three entities: Brain, Robot, and Interaction, depicting their internal relationships. We especially examine interaction modes between human brains and robots, an aspect not yet fully explored. Within this model, we scrutinize and classify current research, extract insights, highlight challenges, and offer recommendations for future studies. Our findings provide a structured design space for human-robot interaction (HRI), informing the development of more efficient BRI frameworks.