  Compositional learning, mastering the ability to combine basic concepts and
construct more intricate ones, is crucial for human cognition, especially in
human language comprehension and visual perception. This notion is tightly
connected to generalization over unobserved situations. Despite its integral
role in intelligence, there is a lack of systematic theoretical and
experimental research methodologies, making it difficult to analyze the
compositional learning abilities of computational models. In this paper, we
survey the literature on compositional learning of AI models and the
connections made to cognitive studies. We identify abstract concepts of
compositionality in cognitive and linguistic studies and connect these to the
computational challenges faced by language and vision models in compositional
reasoning. We overview the formal definitions, tasks, evaluation benchmarks,
variety of computational models, and theoretical findings. We cover modern
studies on large language models to provide a deeper understanding of the
cutting-edge compositional capabilities exhibited by state-of-the-art AI models
and pinpoint important directions for future research.
