Image captioning is a challenging modality transformation task in computer vision and natural language processing, aiming to understand the image content and describe it with a natural language. Recently, the relationship information between objects in the image has been investigated to be of importance in generating a more vivid and readable sentence. Many types of research have been done in relationship mining and learning for leveraging into the caption models. This paper mainly summarizes the methods of relational representation and relational encoding in image captioning. Besides, we discuss the advantages and disadvantages of these methods and provide commonly used datasets for the relational captioning task. Finally, the current problems and challenges in this task are highlighted.