In recent years new technologies for DNA sequence widened research of the roles of tandem repeats in eukaryotes, especially ones that are located in centromere region in chromosomes because of their importance for chromosome segregation, microtubule attachment to kinetochores and, as recently showed, their role in some diseases such as cancers. For identification of tandem repeats and higher order repeats (HORs) we use Global Repeat Map (GRM) algorithm and AlphaSub (ASu) algorithm, developed at Department of Physics, Faculty of Science, University of Zagreb. Here we present some illustrative results obtained using this tool. Based on analysis of DNA sequences, we create a database including information on location, length and divergence for alpha satellite arrays and HORs in human, Neanderthal and chimpanzee genomes (at link http://genom.hazu.hr). We summarize analysis of alpha satellite HORs for human Y chromosome, as well as for some other HORs identified in human and other primates’ chromosome 1 with novel comparison of ~1.6 kb monomer units in them. We also show preliminary results of GRM analysis of three breast cancer exomes. In this respect, we emphasize a need for employing new sequencing methods to determine complete genome assemblies for identification of more precise HOR structures.