Transposable element (TE)-derived sequences are ubiquitous in most eukaryotic genomes known to date. Because their expression and mobility can lead to genomic instability, several pathways have evolved to control TEs. Nevertheless, TEs represent an important source of genomic novelty and are often co-opted for novel functions that are relevant for phenotypic divergence and adaptation. Here, we review how animals, in particular vertebrates, mitigate TE mobility and expression, alongside known examples of TE domestication. We argue that the next frontier is to understand the determinants and dynamics of TE domestication: how they shift from 'non-self' targets of epigenetic silencing to 'self' genetic elements. New technologies enable avenues of research that may close the gap between epigenetic silencing and domestication of TEs.