Substantial progress has been realized in the past several years in our understanding of the molecular mechanisms responsible for the expansions and deletions (genetic instabilities) of repeating tri-, tetra- and pentanucleotide repeating sequences associated with a number of hereditary neurological diseases. These instabilities occur by replication, recombination and repair processes, probably acting in concert, due to slippage of the DNA complementary strands relative to each other. The biophysical properties of the folded-back repeating sequence strands play a critical role in these instabilities. Non-B DNA structural elements (hairpins and slipped structures, DNA unwinding elements, tetraplexes, triplexes and sticky DNA) are described. The replication mechanisms are influenced by pausing of the replication fork, orientation of the repeat strands, location of the repeat sequences relative to replication origins and the flap endonuclease. Methyl-directed mismatch repair, nucleotide excision repair, and repair of damage caused by mutagens are discussed. Genetic recombination and double-strand break repair advances in Escherichia coli, yeast and mammalian models are reviewed. Furthermore, the newly discovered capacities of certain triplet repeat sequences to cause gross chromosomal rearrangements are discussed.