How does order emerge from disorder? This profound question has concerned scientists for many decades.Recently, the emerging field of nanotechnology has stimulated renewed interest in ordering processes,through the idea of self-assembly. Compared with simple assembly processes, in which a product is builtup from appropriately designed components, self-assembly is a more unusual effect. If components can bedesigned carefully enough, then they can assemble themselves spontaneously into ordered products.Such proceses seem surprising, since both intuition and physical laws tell us that systems should becomemore disordered over time: that is, we expect entropy to increase. However, spontaneously ordered productsare familiar in nature: symmetric snowflakes fall from the sky, and faceted gemstones form under the earth.These effects demonstrate that self-assembly can occur, under the right conditions. (The reduced entropy ofthe product is compensated by an increase in the entropy of its environment.)While snowflakes and gemstones are large enough to be seen with the naked eye, several aspects of modernscience are concerned with the self-assembly of much smaller objects, with sizes ranging from a millionth toa thousandth of a millimeter. In biology, self-assembly of such structures can be essential, allowing cells toorganise and control various processes that are required for life. On the other hand, self-assembly of virusesis essential for viral reproduction, but it allows diseases to spread, and is extremely undesirable from the pointof view of the infected organism. In other fields such as physics and chemistry, scientists are often concernedwith assembling large-scale ordered structures, to achieve particular electronic or mechanical properties. Self-assembled solar cells and even self-assembled computers have been proposed.The aim of this research is to develop generally applicable methods for controlling self-assembly. To achievethis, I will focus on the competition between ordered products and unwanted disordered structures. Clearly,disordered raindrops and rocks are much more common in nature than ordered snowflakes and gemstones.These common disordered structures are consistent with our intuitive expectation that entropy increaseswith time. To avoid getting trapped in these disordered states, physicists can draw inspiration from biology, whereassembly processes have been optimised by evolution, in order to achieve high-quality ordered products such as viruses, organelles and cellular skeletons.Statistical physics provides the natural language in which to discuss the competition between order anddisorder. In particular, a central theme of this work is a link between effective assembly and subtle time-reversalsymmetries inherent in the assembly process. That is, intrinsically irreversible self-assembly processes canbe optimised by exploiting the inherent reversibility in Newton's laws of motion. If a system starts to form a disorderedstructure, reversibility allows it to retrace its steps and correct its mistakes, making progress towards the assembledproduct. In order to understand the importance of this effect and its implications, I will combine mathematical and analytic methods with computer simulations of model systems. Initially concentrating on generic features of biological self-assembly processes, I will discuss how physical scientists might adapt or mimic these biological systems, in order to engineer novel ordered products.