What styles of verandas are popular at the moment?

All different depending on location. Check "houzz.com" for ideas.

This is a world site. I for instance can't have a tropical veranda. Because of harsh winters, I'm lucky that my bluestone patio is OK each spring.
There is a trend of outdoor kitchens, way beyond the outdoor grill or fireplace.
I personally like pergolas, or pergola style 'roofs' over a veranda attached to the house, and think they are always popular.