Princess tree (Paulownia tomentosa) has large heart shape leaves, showy purple flowers in spring, and rounded woody seed pods. This invasive tree was once thought to be of potential economic benefit as a timber product in the United States however it has had detrimental consequences to native habitat.
All species of privet (Ligustrum sp.) are nonnative to the United State and several are common invasive species such as Chinese privet (Ligustrum sinense) and common privet (Ligustrum vulgare). Privet is still commonly sold as an ornamental hedge for its quick growth and for the winter color of its blue berries however seeds are rapidly disbursed into the wild.