Tandem amino acid repeats, also known as homopolimeric tract or homopeptides, are very common features of eukaryotic genomes and are present in nearly one-fifth of human encoded proteins. These structures have attracted much interest in the early 1990s when a number of neurological diseases associated with repeat expansion mutations were discovered in humans. Despite their abundance in coding proteins, little is known about their functional consequences. Two scenarios have been proposed. In one, tandem amino acid repeat is considered a neutral structure generated by slippage event and eventually tolerated in protein as long as it does not disrupt the protein function. However, an increasing number of studies proposed that tandem amino acid repeats may be involved in important functional or structural roles. For instance, tandem amino acid repeats had been found to be especially abundant in transcription factors and developmental proteins, where they can potentially modulate protein-protein interaction, exert an effect on gene transcriptional activity, or act as spacer between different protein domains. In addition, several studies have linked changes in repeat size to modification in developmental processes. Despite the advancement made in the last decade, little is known about the selective forces that shape their evolution. The aim of this thesis has been to gain further insight onto the evolutionary dynamics of tandem amino acid repeats by studying the different types of mutations that occur in the amino acid component of the human proteome, by studying the relationship between variability and abundance of amino acid tandem with the evolutionary constraints operating on the proteins, and by studying their conservation and distribution across various vertebrate genomes in both coding and non-coding sequences. The integration of these approaches enabled us to outline an evolutionary model of these structures.