Polymers are macromolecules built from chains of subunits. Most synthetic polymers are built from a single subunit, the monomer, and are termed homopolymers. The connection of two or more homopolymer chains into a larger macromolecule is termed a block copolymer and these can be made with multiple components connected into both linear or branched molecular architectures. Block copolymers remain a subject of significant research interest owing to the control and reproducibility of physical properties and the many fascinating nanoscale structures which can be obtained via self-assembly. The self-assembly behaviour of block copolymers originate from the tendency of the various polymer chains to undergo phase separation which is inherently constrained due to the molecular connectivity. This leads to the formation of ordered mesostructures with characteristic length scales on the order of the chain sizes, typically tens of nanometers. Here the focus is on the molecular architecture as a topological variable and how it influences the morphologies one finds in self-assembled block copolymer systems. We present a range of examples of morphologies with different and sometimes very complex mesoscale topology, i.e. patterns which emerges from the tendency of these molecules to undergo spatial phase separation.