The eukaryotic genome contains a large amount of tandem repeated sequences. Among these repeats, telomere and the centromere are two unique structures on a chromosome, which play an important role in maintaining the stability and function of the genome. A telomere is repetitive nucleotide sequences that located at the ends of chromosomes, which protects the chromosome from deterioration or fusion with another chromosome. Although the repetitive sequences of telomeres in different species are different, telomeres share the same structure. The typical structure of telomere consists of the D-loop and T-loop, which are protected by Shelterin complex. The telomere length is preserved by the enzyme telomerase which elongates telomeres through its reverse transcription activity. It has been widely accepted that telomere attrition is related to aging and cancer. The centromere is a region of the chromosome, which ensures correct separation of daughter chromosomes during cell division. According to the position on the chromosome, the centromere is classified into metacentric, submetacentric, acrocentric, telocentric and holocentric. It can also be divided into point centromere, regional centromere and holocentromere due to the characteristics of the repetitive sequences, in line with the characteristics of the centromeric repetitive sequences. The damaged centromere can cause a large number of chromosomal anomalies such as chromosome rearrangements and breaks, multi-branched chromosomes, and whole-arm deletions, etc. These abnormal chromosomes will lead to serious diseases, such as cancer, ICF syndrome, even cell death. Both the telomere and centromere are composed of highly repetitive sequences and combined with a variety of proteins to form a complex structure. Because of their numerous repetitive DNA sequences, accurate DNA sequencing of telomere and centromere is technically difficult. So there are still many unanswered questions regarding their functions and their working mechanisms. This paper briefly reviews the history of discovering telomere and centromere, the structural characteristics of the telomere and centromere, including the difference of telomere and centromere DNA sequences among different species, the functions of specific proteins binding in these regions. This review also emphasizes the relationships between the repetitive sequences and aging, ICF syndrome or the occurrence of diseases, especially cancer. At last, the paper highlights and prospects the hot research topics in telomere and centromere studies, such as the methods of telomere length measurement, studies on the characteristics of telomerase, and research about centromere repetitive sequence. Hopefully, the fast development of research technology including sequencing technics will help to further understand the biological roles of telomere and centromere, thus facilitate tumor treatment and aging research.