With the rapid development of digital information, the data volume generated by humans and machines is growing exponentially. Along with this trend, machine learning algorithms have been formed and evolved continuously to discover new information and knowledge from different data sources. Learning algorithms using hyperboxes as fundamental representational and building blocks are a branch of machine learning methods. These algorithms have enormous potential for high scalability and online adaptation of predictors built using hyperbox data representations to the dynamically changing environments and streaming data. This paper aims to give a comprehensive survey of literature on hyperbox-based machine learning models. In general, according to the architecture and characteristic features of the resulting models, the existing hyperbox-based learning algorithms may be grouped into three major categories: fuzzy min-max neural networks, hyperbox-based hybrid models, and other algorithms based on hyperbox representations. Within each of these groups, this paper shows a brief description of the structure of models, associated learning algorithms, and an analysis of their advantages and drawbacks. Main applications of these hyperbox-based models to the real-world problems are also described in this paper. Finally, we discuss some open problems and identify potential future research directions in this field.