This review describes a novel type of genome instability, expansion of trinucleotide repeats. Originally discovered in 1991 upon cloning the gene responsible for the fragile X syndrome, it appeared to be a general phenomenon responsible for a growing number of human neurological disorders. Besides apparent medical importance, the discovery of trinucleotide repeat expansion unraveled a fundamental problem of human genetics: a non-Mendelian type of inheritance called anticipation. Understanding the mechanisms of repeat expansion and the molecular pathways leading from these expansions to human diseases became a formidable task for modern biology and one of its spectacular achievements. Here we discuss the major breakthroughs in this field made during the last decade with an emphasis on molecular models of repeat expansion.