The concepts of size and scale are of fundamental importance in science, engineering and technology, and occupy a central place in human experience and thought. Size and shape are crucial properties of physical and abstract objects, while scale and dimension are basic descriptive tools that we employ to compare them. Understanding the dependence of physical phenomena on size and scale allows us to develop predictive tools that form the core of design and enable the creation of artefacts and technological systems. Of particular interest to us are situations when the size dependence turns out to be complex, characterized by changes and transitions in behaviour between different scales, e.g. laboratory and full scale prototypes, nano-scale objects as opposed to macroscopic, etc. Scaling transitions and size effects in the fracture and strength of materials and structures have particular significance in modern science and engineering. The boundaries of scale of the mechanical phenomena studied and devices exploited are expanding, on the one hand, towards global scale phenomena, and on the other towards the nanometre scale processes. These circumstances challenge the conventional wisdom acquired over many decades, according to which laboratory experiments performed at the engineering scale (sub-mm to a few meters) provide the source of material property data then used as input for modelling at the scale of the real object. When deviations from accepted scaling laws are found, new physical deformation mechanisms need to be proposed or identified, and new modelling approaches to be developed and validated. In this paper I review some examples of non-trivial size dependence, and address a fundamental question of the efficient description of size effects and scale transitions. The functional description of multi-scaling power law regimes is considered, and the functional form suitable for the task is identified. This form is then applied to a variety of experimental data manifesting size effects, including dual failure strength criteria (stress and toughness), fatigue crack growth thresholds (Kitagawa-Takahashi diagram) and applications in the context of fretting fatigue, Paris fatigue crack growth law, hardness of coated systems, etc.