Here are some design notes when it comes to modern pergola designs. The most common pergola design is to have decorative and somewhat rounded ends on the beam. The easiest way of creating a more modern pergola is to do away with the decorative ends.
structure: I like the cube look, but Aron worries about it not being united with house rooflines. Chunky black timber pergola and lime washed deck. Pinned to Garden Design - Pergolas by Darin Bradbury.