Many plants are so easy to grow that they become invasive weeds. Butterfly bush, Buddleja davidii, has done exactly that in some regions, and is only controlled here by the arid climate. Yet, once established, it does not need much water at all, and can survive on rainfall in some spots. They only want good sun exposure.
Mature plants can get more than 15-feet tall and half as broad, with long arching limbs. Most garden varieties stay smaller, and some do not get much more than six feet tall. The evergreen foliage is sage green, grayish green or chartreuse. The paired leaves are about the size and shape of willow or eucalyptus leaves.
Conical trusses of densely packed tiny flowers that bloom in mid-summer can be various shades of blue, purple, red and pink, as well as dusty white. Some new varieties bloom soft orange or yellowish orange. The more compact and colorful modern varieties are not as fragrant as old classics are.
Tony Tomeo 
I am a lover of buddleia and have had all colours in my garden. Some of my bushes arrived from seed disposal. I noticed that the species grows according to their colour. I now have only one bush, a pink delight. I chose that one as it really grows as a compact bushes and does not produce such long branches as the darker mauve colour. I also had a nice blue buddleia for some time. Of course one of the main reasons for my love of the bush is the attaction it has for butterflies. They see to get high on the flowers and gives a good opportunity for some good photos. I remember my visits to England, I often saw them growing wild next to the railway tracks.
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They might have naturalized in England. They have become aggressively invasive in some regions. Although the self sow here, they do not seem to naturalize too aggressively.
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I have head that these are invasive but in my climate we can’t cut them back in autumn for fear of losing them. And after a particularly harsh winter, I lost mine altogether. It was ‘Dark Knight,’ one of the largest and darkest of the purples. I haven’t replanted.
Karla
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They have naturalized in some favorable regions, and in some regions, are aggressively invasive. They self sow here, but do not seem to be aggressively invasive, or even naturalized.
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I love butterfly bush! True to their name, they attract lots of pollinators to our garden. I have four different ones, including a dwarf variety. I always had heard they could become invasive, but never saw any sign of it until we traveled to London a few years ago. I saw them all along the train tracks and highways. I guess if it’s going to be invasive, the least it could do is be pretty!
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Someone mentioned that. I would not have guessed that England would be a place for them to naturalize. They self sow here, but do not seem to naturalize.
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I really like them. I’ve seen them growing in abandoned parking lots and they cheer things up.
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They are naturalized in a few places. Once established, they are not at all demanding, so will do well even if abandoned.
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I’ve tried to grow some of the dwarf varieties, but they haven’t lasted long.
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Were they the ‘Proven Winners’ cultivars?
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I think so – one was ‘Blue Chip’, maybe? God, my memory is terrible.
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That would make sense. I was not impressed with that one, or related cultivars, either.
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