Expanded tandem repeat DNAs are associated with various unusual chromosomal lesions, despiralizations, multi-branched inter-chromosomal associations, and fragile sites. Fragile sites cytogenetically manifest as localized gaps or discontinuities in chromosome structure and are an important genetic, biological, and health-related phenomena. Common fragile sites (∼230), present in most individuals, are induced by aphidicolin and can be associated with cancer; of the 27 molecularly-mapped common sites, none are associated with a particular DNA sequence motif. Rare fragile sites (≳ 40 known), ≤ 5% of the population (may be as few as a single individual), can be associated with neurodevelopmental disease. All 10 molecularly-mapped folate-sensitive fragile sites, the largest category of rare fragile sites, are caused by gene-specific CGG/CCG tandem repeat expansions that are aberrantly CpG methylated and include FRAXA, FRAXE, FRAXF, FRA2A, FRA7A, FRA10A, FRA11A, FRA11B, FRA12A, and FRA16A. The minisatellite-associated rare fragile sites, FRA10B, FRA16B, can be induced by AT-rich DNA-ligands or nucleotide analogs. Despiralized lesions and multi-branched inter-chromosomal associations at the heterochromatic satellite repeats of chromosomes 1, 9, 16 are inducible by de-methylating agents like 5-azadeoxycytidine and can spontaneously arise in patients with ICF syndrome (Immunodeficiency Centromeric instability and Facial anomalies) with mutations in genes regulating DNA methylation. ICF individuals have hypomethylated satellites I-III, alpha-satellites, and subtelomeric repeats. Ribosomal repeats and subtelomeric D4Z4 megasatellites/macrosatellites, are associated with chromosome location, fragility, and disease. Telomere repeats can also assume fragile sites. Dietary deficiencies of folate or vitamin B12, or drug insults are associated with megaloblastic and/or pernicious anemia, that display chromosomes with fragile sites. The recent discovery of many new tandem repeat expansion loci, with varied repeat motifs, where motif lengths can range from mono-nucleotides to megabase units, could be the molecular cause of new fragile sites, or other chromosomal lesions. This review focuses on repeat-associated fragility, covering their induction, cytogenetics, epigenetics, cell type specificity, genetic instability (repeat instability, micronuclei, deletions/rearrangements, and sister chromatid exchange), unusual heritability, disease association, and penetrance. Understanding tandem repeat-associated chromosomal fragile sites provides insight to chromosome structure, genome packaging, genetic instability, and disease.