The evolution of complex topological structures in mesoscale systems is an important motif in modern condensed matter physics and has a strong influence of technology. In this talk, I will provide an overview of our work on complex fluids by focusing on two examples: the blue phases of liquid crystals and shear flow in binary fluids. The blue phases of liquid crystals were once discribed as "totally useless", but are now appearing in prototype displays, example. A fundamental understanding of how their complex structure influences optical properties is therefore important. The second example may also be regarded as "totally useless", and is an attempt to understand the fundamental behaviour of binary fluids under shear. Another common strand in these examples is the use of a highly parallel lattice Boltzmann method for the hydrodynamic part of the problem.