Eukaryotic genomes are organized in 3D in a multi-scale manner, and different mechanisms acting at each of these scales can contribute to transcriptional regulation. However, the large single-cell variability in 3D chromatin structures represent a challenge to understand how transcription may be differentially regulated between cell types in a robust and efficient manner. Here, we describe the different mechanisms by which 3D chromatin structure was shown to contribute to cell type-specific transcriptional regulation. Excitingly, several novel methodologies able to measure 3D chromatin conformation and transcription in single cells in their native tissue context, or to detect the dynamics of cis-regulatory interactions, are starting to allow quantitative dissection of chromatin structure noise and relate it to how transcription may be regulated between different cell types and cell states.