Fundamental investigations into mechanical behaviour and properties, e.g. elasticity, plasticity, hardness, toughness, strength and failure, exhibited at the nanoscale have increased rapidly in number and in breadth over the past two decades as experimental techniques and theoretical treatments have advanced. This review covers selected contemporary nanomechanics research and gives an overview of some fundamental questions, measurement challenges and opportunities concerning nanostructured materials, their mechanical properties and deformation mechanisms -particularly, relationships with size-scale phenomena. Significant theoretical developments are mentioned in relevant sections and advances in computational modelling are considered briefly, including perspectives on the current state and gaps between complete and rigorous simulations for mechanical behaviour in nanomaterials and experimental data to qualify certain predictive calculations. We categorise the study of mechanics by nanomaterial types from primary objects (i.e. single nanoscale elements like nanofibres and nanopillars), simple composites and other extended nanostructures like films and multilayers to complex natural and synthetic systems ranging from biological cells and mineralised biocomposites to nanoelectromechanical systems and DNA nanorobots. The future outlook and concluding remarks summarise general areas of open knowledge in the field and include a call for increased collaboration between experiments and modelling for the fruition of twenty-first century advancements and exploration.