Transposable elements (TEs) make up the most abundant and dynamic component of plant genomes and they represent important sources of evolutionary novelty. Despite these common genomic features among plants, fundamental questions about TE evolution are still poorly understood, in part because so few plant species have been characterized in a phylogenetic framework with respect to TEs. An important objective therefore is to understand the specific contributions of TEs in a large number of plant species in order to construct a more complete picture of evolution in the plant kingdom. In this work, I present novel computational methods and software for analyzing TEs in unexplored genomes, and I demonstrate the utility of these developments by explaining patterns of TE evolution in the plant family Asteraceae. The Asteraceae is the largest family of flowering plants, and has very recent evolutionary origin. These features, along with a global distribution of species adapted to many different environments, make this family an excellent system to investigate evolutionary processes. By using a novel repeat finding method described herein, I show that Asteraceae genomes differ in the abundance and diversity of TEs from the most closely related family Calyceraceae, and each subfamily of the Asteraceae exhibits unique patterns of TE evolution. From the base of the family to the most derived lineages of the Asteraceae, there is a linear increase in the amount of one type of TE, Gypsy, and there is a linear decrease in the amount of Copia TEs. This pattern is driven, in part, by a marked increase in the genomic dominance of certain Gypsy TE families at the base of tribe Heliantheae, and these events have lead to a decrease in the diversity of TEs in this tribe. Contrary to the near universal species-area relationship in ecological studies, I show that larger genomes may be a product of unequal contributions of TE families and do not necessarily support a greater diversity of TEs. Taken together, these findings highlight the importance of broad taxonomic sampling in a phylogenetic framework for understanding the mechanisms contributing to the evolution of TEs across the plant kingdom.