The hierarchical three-dimensional folding of the mammalian genome constitutes an important regulatory layer of gene expression and cell fate control during processes such as development and tumorigenesis. Accumulating evidence supports the existence of complex topological assemblies in which multiple genes and regulatory elements are frequently interacting with each other in the 3D nucleus. Here, we will discuss the nature, organizational principles, and potential function of such assemblies, including the recently reported enhancer “hubs,” “cliques,” and FIREs (frequently interacting regions) as well as multi-contact hubs. We will also review recent studies that investigate the role of transcription factors (TFs) in driving the topological genome reorganization and hub formation in the context of cell fate transitions and cancer. Finally, we will highlight technological advances that enabled these studies, current limitations, and future directions necessary to advance our understating in the field.