Transposable elements (TEs) constitute the majority of angiosperm DNA, but the processes that govern their accumulation remain mysterious. Here we discuss the three major forces that govern the accumulation of TEs, corresponding to the three panels of a triptych. The first force, transposition, creates new copies of TEs, but is regulated by both host- and TE-specific mechanisms. The second force, deletion of TE DNA, is capable of removing vast swaths of genomic regions via recombinational processes, but we still have very little insight into how deletion varies across species and even among TE types. Finally, we focus on the often-ignored third panel of our triptych – the population processes that determine the ultimate evolutionary fate of TE insertions.