Tandem repeats of various trinucleotide motifs are frequent entities in transcripts, and RNA structures formed by these sequences depend on the motif type and number of reiterations. The functions performed by normal triplet repeats in transcripts are poorly understood, but abnormally expanded repeats of certain types trigger pathogenesis in several human genetic disorders known as the triplet repeat expansion diseases (TREDs). The diseases caused by expanded non-coding CUG and CGG repeats in transcripts include myotonic dystrophy type 1 and fragile X-associated tremor ataxia syndrome. Another group of disorders in which transcripts containing translated CAG repeats play an auxiliary role in pathogenesis include Huntington’s disease and several spinocerebellar ataxias. In this review, we gathered existing knowledge regarding the structural features of triplet repeats in transcripts and discussed this in the context of various pathogenic mechanisms assigned to toxic RNA repeats. These mechanisms include aberrant alternative splicing, the inhibition of nuclear transport and export, induction of the innate immune response, alteration of a microRNA biogenesis pathway and abnormal activation of an RNA interference pathway. We also provide ideas for future investigations to reveal further mechanisms of pathogenesis directly triggered by mutant RNA repeats in TREDs.