Abrasion is a form of wear prominent particularly in the agricultural, mining, mineral and transportation industries. The cost of abrasive wear to the national economy is estimated to be about 1% of the gross national product, and it can compromise the safety and reliability of engineering components. The mechanism of wear is complex and dependent on all the materials involved in the process, environmental conditions and many subtle factors such as the shape of the abrading particles. Many abrasion-resistant steels are based on a quenched and tempered martensitic microstructure, because the hardness of the steel should intuitively matter in determining the wear rate. Nevertheless, the relationship between the rate of material loss and steel hardness is unlikely to be monotonic. The purpose of the work presented in this thesis was primarily to study the abrasive wear behavior of a nanostructured bainitic steel that has been successful in structural applications, is capable of mass production, and can achieve hardness levels comparable to martensitic steels without compromising ductility, toughness and fatigue resistance. A variety of wear mechanisms have been studied, in each case with a detailed characterisation of the damage, the structural evolution and a panoply of theoretical approaches. In the case of three-body abrasion, it is found that huge variations in hardness, achieved by changing the structure from pearlite, nanostructured bainite to martensite by heat treatment, do not lead to significant differences in the wear rate. This is because the wear mechanisms change, for example from severe sub-surface deformation leading to sticking in the case of pearlite, to brittle detachment of material in the martensitic state. The nanostructured bainite, on the other hand, undergoes reaustenitisation at the surface that leads to the formation of a fine martensitic layer with consequent surface hardening, in contrast to the pearlite and martensite, both of which soften at the contact surfaces. It is the presence of stable austenite in the nanostructured bainite that causes this difference, because austenitisation becomes easier to achieve. This hypothesis has been further tested by eliminating the austenite from the nanostructured bainite. The experiments confirm that a reaustenitised layer no longer forms during three-body abrasion. The softening observed on martensitic samples also disappears when similar tests are done on tempered martensite, indicating the effect of the localised heat generated during dry abrasion on untempered martensite. In contrast to three-body abrasion using silica where the weight loss is insensitive to hardness, the nanostructured bainite outperforms most commercial alloys of equivalent hardness, and sometime even harder materials, during dry rolling/sliding wear. The mechanisms involved have been rationalised in terms of structural damage mechanisms, the development of beneficial residual stresses, and detailed changes in crystallite size and dislocation character as a function of rolling. It has, in general, been possible to rationalise the observed variations in different types of wear tests and micro- or nanostructures, and it is believed that the work will be of use in designing commercially important products.