Chromatin has distinct three-dimensional (3D) architectures important in key biological processes, such as cell cycle, replication, differentiation, and transcription regulation. In turn, aberrant 3D structures play a vital role in developing abnormalities and diseases such as cancer. This review discusses key 3D chromatin structures (topologically associating domain, lamina-associated domain, and enhancer–promoter interactions) and corresponding structural protein elements mediating 3D chromatin interactions [CCCTC-binding factor, polycomb group protein, cohesin, and Brother of the Regulator of Imprinted Sites (BORIS) protein] with a highlight of their associations with cancer. We also summarise the recent development of technologies and bioinformatics approaches to study the 3D chromatin interactions in gene expression regulation, including crosslinking and proximity ligation methods in the bulk cell population (ChIA-PET and HiChIP) or single-molecule resolution (ChIA-drop), and methods other than proximity ligation, such as GAM, SPRITE, and super-resolution microscopy techniques.