The transport of objects in microfluidic arrays of obstacles is a surprisingly rich area of physics and statistical mechanics. Tom Duke's mastery of these areas had a major impact in the development of biotechnology which uses these ideas at an increasing scale. We first review how biological objects are transported in fluids at low Reynolds numbers, including a discussion of electrophoresis, then concentrate on the separation of objects in asymmetric arrays, sometimes called Brownian ratchets when diffusional symmetry is broken by the structures. We move beyond this to what are called deterministic arrays where non-hydrodynamic forces in asymmetric arrays allow for extraordinary separation, and we look to the future of using these unusual arrays at the nanoscale and at the hundreds of micrometre scale. The emphasis is on how the original ideas of Tom Duke drove this work forward.