In science and engineering the concepts of size and scale play a key role in design. Many physical phenomena show a dependence on the size of objects and the scale of consideration. Of particular interest to the present study are the situations when the dependence of system response on the size appears to be complex, insofar as it is characterized by transitions in behaviour between different scales. Of particular importance is the connection between laboratory specimens and full scale objects and systems. In the context of modern technology, of increasing interest is the behaviour of nano-scale objects as opposed to macroscopic. 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 and applications in the context of fretting fatigue, the Paris fatigue crack growth law, etc.