This must be one of the sillier horticultural names. Tree houseleek, Aeonium arboreum, is neither a tree nor related to leeks. The biggest cultivars can not stand much more than three feet tall. Above that, their succulent foliage gets too heavy for their fleshy stems and fine roots. They perform well as houseplants only within very sunny situations.
Formerly common tree houseleek, with simple green foliage, is not so common anymore. Almost all popular modern cultivars are variegated or bronzed, with wide foliar rosettes. Variegation ranges from bright lemony yellow to creamy white. Bronze ranges from light brown to very darkly purplish. Foliar rosettes are about four to eight inches wide.
Plumply conical trusses of tiny yellow or chartreuse flowers bloom for spring. They are neither numerous nor brightly colorful, but are weirdly interesting. Fresh spring foliage is most colorful and lush. It can fade and partially shed during arid summer weather. New plants propagate very easily from dragging stems or cuttings of pruning scraps.
Tony Tomeo 
I have this, with bronze leaves, in my succulent collection. All winter it lives in my daughter’s bedroom window which faces east, and remains mostly dormant. It lives outside in the summer in almost full sun. It’s most active in late summer/early fall when the nights are cooler and it gets some rain.
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I’ve never seen it bloom.
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The common green sort in my planter box downtown did not bloom for a few years, and when it did, it was more weird than appealing. It was easier to cut the entire bloomed stem out after bloom than to cut the deteriorated bloom off and just let new growth develop a tuft of new growth on the end of the branch like that. The bronze cultivar in the same planter box was stolen before it bloomed.
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They live outside all year here, but get sparse during the warm and arid weather of summer. They are remarkably adaptable.
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