Transposable elements are known by many names, including 'transposons', 'interspersed repeats', 'selfish genetic elements', 'jumping genes', and 'parasitic DNA', but here we will refer to them simply as TEs. Many biologists will have heard of TEs and their ability to transpose (change position) within the genome. But fewer may be aware of their varied influences on host biology, including contributions to the evolution of diverse host traits such as internal gestation, memory, colouration, and adaptive immunity. TEs are a near ubiquitous feature of eukaryotic genomes, and they often comprise a substantial proportion of total genomic content. Consequently, TE genes are considered among the most abundant coding sequences in nature. Recent advances in genome sequencing offer a golden age for TE research, providing opportunities to greatly improve understanding of interactions with host evolution and disease. However, significant challenges remain in our ability to detect and analyse TEs, which impair efforts to decipher their evolution, characterise their diversity, and elucidate their myriad host influences. Below, we summarise key aspects of TE biology and discuss major outstanding research questions.