Repetitive DNA sequences, comprising up to 50% of the genome in all eukaryotes, play important roles in a wide range of cellular functions, such as transcriptional regulation, genome stability and cellular differentiation. However, due to technical difficulties in differentiating their sequences, DNA repeats remain one of the most mysterious parts of eukaryotic genomes. Key questions, such as how repetitive entities behave at individual level and how the internal architecture of these repeats is organized, are still poorly understood. Recent advances from our group reveal unexpected position-dependent variation within tandem DNA repeats in fission yeast. Despite sharing identical DNA sequences, the peri-centromeric repeats are organized into diverse epigenetic states and chromatin structures. We demonstrate that this position-dependent variation requires key heterochromatin factors and condensin. Our works further suggest that the peri-centromeric repeats are organized into distinct higher-order structures that ensure proper positioning of CENP-A, the centromere-specific histone H3 variant, to centromeres. These most recent developments offer insights into the mechanisms underlying the position effect within tandem DNA arrays, and have broad implications in the field of epigenetics and chromatin biology.