Diblock copolymer melts present a physical paradigm for periodic phase separation. On the other hand, a simple model gives rise to a nonlocal functional which itself is a mathematical paradigm for energy-driven pattern formation associated with short and long-range interactions. In this talk, I will discuss several mathematical aspects associated with the functional and the underlying physical problem. These will include modeling, analysis of periodicity and scale, numerics, and the geometry on minimizing structures. I will then focus on this last issue, presenting some very recent results obtained with P. Sternberg (Indiana).