I'm kinda meh about roof gardens/ grass roofs bc they can accumulate a lot of weight and collapse/ cause leaks
But living walls? Mighty sexy
They provide natural insulation, which not only keeps the heat in during cold days, but keeps the heat out during hot ones. It's better planned and maintained than vines (depending on the plant ofc).
Flooding in urban areas can be reduced since the roots and the growing medium will hold in moisture. Air can be purified, and heat can be reduced because of evaporation.