Regulation of gene expression in eukaryotes involves many complex processes, in which chromatin structure plays an important role. In addition to the epigenetic effects, such as DNA methylation and phosphorylation or histone modifications, gene expression is also controlled by the spatial organization of chromatin. For example, distant regulatory elements (enhancers, insulators) may come into direct physical interaction with target genes or other regulatory elements located in genomic regions of up to several hundred kilobases in size. Such long-range interactions result in the formation of chromatin loops. In the last several years, there has been a rapid increase in our knowledge of the spatial organization of chromatin in the nucleus through the chromosome conformation capture (3C) technology. Here we review and compare the original 3C and 3C-based methods including chromosome conformation capture-on-chip (4C), chromosome conformation capture carbon copy (5C), hi-resolution chromosome confomation capture (HiC). In this article, we discuss different aspects of how the nuclear organization of chromatin is associated with gene expression regulation and how this knowledge is useful in translational medicine and clinical applications. We demonstrate that the knowledge of the chromatin 3D organization may help understand the mechanisms of gene expression regulation of genes involved in the development of human diseases, such as CFTR (responsible for cystic fibrosis) or IGFBP3 (associated with breast cancer pathogenesis). Additionally, 3C-derivative methods have been also useful in the diagnosis of some leukemia subtypes.