Expansions of gene-specific DNA tandem repeats (TRs), first described in 1991 as a disease-causing mutation in humans, are now known to cause >60 phenotypes, not just disease, and not only in humans. TRs are a common form of genetic variation with biological consequences, observed, so far, in humans, dogs, plants, oysters, and yeast. Repeat diseases show atypical clinical features, genetic anticipation, and multiple and partially penetrant phenotypes among family members. Discovery of disease-causing repeat expansion loci accelerated through technological advances in DNA sequencing and computational analyses. Between 2019 and 2021, 17 new disease-causing TR expansions were reported, totaling 63 TR loci (>69 diseases), with a likelihood of more discoveries, and in more organisms. Recent and historical lessons reveal that properly assessed clinical presentations, coupled with genetic and biological awareness, can guide discovery of disease-causing unstable TRs. We highlight critical but underrecognized aspects of TR mutations. Repeat motifs may not be present in current reference genomes but will be in forthcoming gapless long-read references. Repeat motif size can be a single nucleotide to kilobases/unit. At a given locus, repeat motif sequence purity can vary with consequence. Pathogenic repeats can be “insertions” within nonpathogenic TRs. Expansions, contractions, and somatic length variations of TRs can have clinical/biological consequences. TR instabilities occur in humans and other organisms. TRs can be epigenetically modified and/or chromosomal fragile sites. We discuss the expanding field of disease-associated TR instabilities, highlighting prospects, clinical and genetic clues, tools, and challenges for further discoveries of disease-causing TR instabilities and understanding their biological and pathological impacts—a vista that is about to expand.